You start at, 10000000000, and you are willing to toss a coin up to , 200, times If the coin lands on Heads you add 1 to the running su, if it lands in Tails\ you add 2 You quit as soon as you hit a prime We will explore this for different loaded coins ---------------------------------------------------- if the prob. of getting a Heads is, 1/100, then The prob. of finishing is, 0.1648471665 The (conditoned) expected duration is, 76.847306028898115602 The (conditoned) standard-deviation of duration is, 54.695339911805010817 The (conditoned) expected distance traveled is, 152.60434918158136302 The (conditoned) standard-deviation of duration is, 109.30312204332387510 The (conditioned) correlation between them is, 0.9999925359 ---------------------------------------------------- if the prob. of getting a Heads is, 1/50, then The prob. of finishing is, 0.03684528207 The (conditoned) expected duration is, 56.557502268531974494 The (conditoned) standard-deviation of duration is, 46.608575529453772164 The (conditoned) expected distance traveled is, 111.88221016383577476 The (conditoned) standard-deviation of duration is, 92.948419018537143712 The (conditioned) correlation between them is, 0.9999740327 ---------------------------------------------------- if the prob. of getting a Heads is, 3/100, then The prob. of finishing is, 0.01082011111 The (conditoned) expected duration is, 44.219550433497706313 The (conditoned) standard-deviation of duration is, 38.911583153751359547 The (conditoned) expected distance traveled is, 87.077499666512624592 The (conditoned) standard-deviation of duration is, 77.371805348316855935 The (conditioned) correlation between them is, 0.9999434146 ---------------------------------------------------- if the prob. of getting a Heads is, 1/25, then The prob. of finishing is, 0.004065725544 The (conditoned) expected duration is, 36.636384349064522289 The (conditoned) standard-deviation of duration is, 32.864095480568168289 The (conditoned) expected distance traveled is, 71.793877385350048418 The (conditoned) standard-deviation of duration is, 65.119575034573192374 The (conditioned) correlation between them is, 0.9998972856 ---------------------------------------------------- if the prob. of getting a Heads is, 1/20, then The prob. of finishing is, 0.001945464344 The (conditoned) expected duration is, 31.757549303358311967 The (conditoned) standard-deviation of duration is, 28.333421559204646821 The (conditoned) expected distance traveled is, 61.921455181122169596 The (conditoned) standard-deviation of duration is, 55.921943211044037473 The (conditioned) correlation between them is, 0.9998323369 ---------------------------------------------------- if the prob. of getting a Heads is, 3/50, then The prob. of finishing is, 0.001142149264 The (conditoned) expected duration is, 28.469743031579046998 The (conditoned) standard-deviation of duration is, 24.972127210021932565 The (conditoned) expected distance traveled is, 55.228342460830603238 The (conditoned) standard-deviation of duration is, 49.073098152892637780 The (conditioned) correlation between them is, 0.9997469613 ---------------------------------------------------- if the prob. of getting a Heads is, 7/100, then The prob. of finishing is, 0.0007531499598 The (conditoned) expected duration is, 26.164978451383026175 The (conditoned) standard-deviation of duration is, 22.476068795725943738 The (conditoned) expected distance traveled is, 50.496512319013027394 The (conditoned) standard-deviation of duration is, 43.957608207524156523 The (conditioned) correlation between them is, 0.9996423563 ---------------------------------------------------- if the prob. of getting a Heads is, 2/25, then The prob. of finishing is, 0.0005188559187 The (conditoned) expected duration is, 24.493722105154701253 The (conditoned) standard-deviation of duration is, 20.602355810436836244 The (conditoned) expected distance traveled is, 47.026559288890227251 The (conditoned) standard-deviation of duration is, 40.087457634266349704 The (conditioned) correlation between them is, 0.9995213798 ---------------------------------------------------- if the prob. of getting a Heads is, 9/100, then The prob. of finishing is, 0.0003631706595 The (conditoned) expected duration is, 23.246214257918511195 The (conditoned) standard-deviation of duration is, 19.167570365023081169 The (conditoned) expected distance traveled is, 44.399226651033147759 The (conditoned) standard-deviation of duration is, 37.095822854414626256 The (conditioned) correlation between them is, 0.9993868459 ---------------------------------------------------- if the prob. of getting a Heads is, 1/10, then The prob. of finishing is, 0.0002578356998 The (conditoned) expected duration is, 22.292603483589546737 The (conditoned) standard-deviation of duration is, 18.042943051003469271 The (conditoned) expected distance traveled is, 42.355172008552034637 The (conditoned) standard-deviation of duration is, 34.725516989702150815 The (conditioned) correlation between them is, 0.9992409782 ---------------------------------------------------- 11 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.0001866232360 The (conditoned) expected duration is, 21.549859741186364906 The (conditoned) standard-deviation of duration is, 17.142104952001853390 The (conditoned) expected distance traveled is, 40.728664449306127983 The (conditoned) standard-deviation of duration is, 32.804006500116071506 The (conditioned) correlation between them is, 0.9990856019 ---------------------------------------------------- if the prob. of getting a Heads is, 3/25, then The prob. of finishing is, 0.0001381707119 The (conditoned) expected duration is, 20.962861861208597839 The (conditoned) standard-deviation of duration is, 16.407265788246799244 The (conditoned) expected distance traveled is, 39.409758493821305984 The (conditoned) standard-deviation of duration is, 31.215819518588953148 The (conditioned) correlation between them is, 0.9989223180 ---------------------------------------------------- 13 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.0001046424545 The (conditoned) expected duration is, 20.493609150239895796 The (conditoned) standard-deviation of duration is, 15.798699585331122095 The (conditoned) expected distance traveled is, 38.322732844017601863 The (conditoned) standard-deviation of duration is, 29.881589414095724567 The (conditioned) correlation between them is, 0.9987525211 ---------------------------------------------------- if the prob. of getting a Heads is, 7/50, then The prob. of finishing is, 0.00008089866718 The (conditoned) expected duration is, 20.115025309339003801 The (conditoned) standard-deviation of duration is, 15.288131769878249477 The (conditoned) expected distance traveled is, 37.413705509506881072 The (conditoned) standard-deviation of duration is, 28.744841577367633838 The (conditioned) correlation between them is, 0.9985773773 ---------------------------------------------------- if the prob. of getting a Heads is, 3/20, then The prob. of finishing is, 0.00006366233203 The (conditoned) expected duration is, 19.807294094525030975 The (conditoned) standard-deviation of duration is, 14.854830026279469668 The (conditoned) expected distance traveled is, 36.643305996314570785 The (conditoned) standard-deviation of duration is, 27.764165746527346335 The (conditioned) correlation between them is, 0.9983978255 ---------------------------------------------------- if the prob. of getting a Heads is, 4/25, then The prob. of finishing is, 0.00005085115413 The (conditoned) expected duration is, 19.555597897702181492 The (conditoned) standard-deviation of duration is, 14.483247114045890292 The (conditoned) expected distance traveled is, 35.982151062230966835 The (conditoned) standard-deviation of duration is, 26.908494810314666686 The (conditioned) correlation between them is, 0.9982146040 ---------------------------------------------------- 17 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.00004112446780 The (conditoned) expected duration is, 19.348661156076378001 The (conditoned) standard-deviation of duration is, 14.161521004983345239 The (conditoned) expected distance traveled is, 35.407929882012515548 The (conditoned) standard-deviation of duration is, 26.154105073987774514 The (conditioned) correlation between them is, 0.9980282877 ---------------------------------------------------- if the prob. of getting a Heads is, 9/50, then The prob. of finishing is, 0.00003360071700 The (conditoned) expected duration is, 19.177777549709219303 The (conditoned) standard-deviation of duration is, 13.880470496946460357 The (conditoned) expected distance traveled is, 34.903457159378702028 The (conditoned) standard-deviation of duration is, 25.482611803897532267 The (conditioned) correlation between them is, 0.9978393225 ---------------------------------------------------- 19 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.00002768683140 The (conditoned) expected duration is, 19.036141015050027688 The (conditoned) standard-deviation of duration is, 13.632897840040348591 The (conditoned) expected distance traveled is, 34.455334336485594977 The (conditoned) standard-deviation of duration is, 24.879580519361526012 The (conditioned) correlation between them is, 0.9976480548 ---------------------------------------------------- if the prob. of getting a Heads is, 1/5, then The prob. of finishing is, 0.00002297573559 The (conditoned) expected duration is, 18.918374432415789051 The (conditoned) standard-deviation of duration is, 13.413092422878844343 The (conditoned) expected distance traveled is, 34.053006582268560476 The (conditoned) standard-deviation of duration is, 24.333540731489418531 The (conditioned) correlation between them is, 0.9974547538 ---------------------------------------------------- 21 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.00001918465934 The (conditoned) expected duration is, 18.820190597983925225 The (conditoned) standard-deviation of duration is, 13.216470698144366408 The (conditoned) expected distance traveled is, 33.688084725924690880 The (conditoned) standard-deviation of duration is, 23.835271921688252965 The (conditioned) correlation between them is, 0.9972596283 ---------------------------------------------------- 11 if the prob. of getting a Heads is, --, then 50 The prob. of finishing is, 0.00001611777990 The (conditoned) expected duration is, 18.738143887601534127 The (conditoned) standard-deviation of duration is, 13.039310858909051324 The (conditoned) expected distance traveled is, 33.353848872013232583 The (conditoned) standard-deviation of duration is, 23.377278384821424475 The (conditioned) correlation between them is, 0.9970628363 ---------------------------------------------------- 23 if the prob. of getting a Heads is, ---, then 100 The prob. of finishing is, 0.00001364239909 The (conditoned) expected duration is, 18.669445609267845950 The (conditoned) standard-deviation of duration is, 12.878556057843871328 The (conditoned) expected distance traveled is, 33.044879557336710657 The (conditoned) standard-deviation of duration is, 22.953399760430006080 The (conditioned) correlation between them is, 0.9968644904 ---------------------------------------------------- if the prob. of getting a Heads is, 6/25, then The prob. of finishing is, 0.00001167066260 The (conditoned) expected duration is, 18.611825249063668386 The (conditoned) standard-deviation of duration is, 12.731670407501992696 The (conditoned) expected distance traveled is, 32.756780672005311625 The (conditoned) standard-deviation of duration is, 22.558524585410101264 The (conditioned) correlation between them is, 0.9966646619 ---------------------------------------------------- if the prob. of getting a Heads is, 1/4, then The prob. of finishing is, 0.00001014144648 The (conditoned) expected duration is, 18.563425530343488372 The (conditoned) standard-deviation of duration is, 12.596537607723034643 The (conditoned) expected distance traveled is, 32.485969824421007784 The (conditoned) standard-deviation of duration is, 22.188385791969459503 The (conditioned) correlation between them is, 0.9964633862 ---------------------------------------------------- 13 if the prob. of getting a Heads is, --, then 50 -5 The prob. of finishing is, 0.9001131869 10 The (conditoned) expected duration is, 18.522722489427541043 The (conditoned) standard-deviation of duration is, 12.471392414382522566 The (conditoned) expected distance traveled is, 32.229518556159600520 The (conditoned) standard-deviation of duration is, 21.839419309777927791 The (conditioned) correlation between them is, 0.9962606750 ---------------------------------------------------- 27 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.8186793514 10 The (conditoned) expected duration is, 18.488463568019323732 The (conditoned) standard-deviation of duration is, 12.354772229896687159 The (conditoned) expected distance traveled is, 31.985028634372887176 The (conditoned) standard-deviation of duration is, 21.508662939979789769 The (conditioned) correlation between them is, 0.9960565351 ---------------------------------------------------- if the prob. of getting a Heads is, 7/25, then -5 The prob. of finishing is, 0.7617904279 10 The (conditoned) expected duration is, 18.459618056466469279 The (conditoned) standard-deviation of duration is, 12.245474490655212264 The (conditoned) expected distance traveled is, 31.750533441261214806 The (conditoned) standard-deviation of duration is, 21.193670137548206492 The (conditioned) correlation between them is, 0.9958509851 ---------------------------------------------------- 29 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.7200569927 10 The (conditoned) expected duration is, 18.435335842800571390 The (conditoned) standard-deviation of duration is, 12.142509369390130307 The (conditoned) expected distance traveled is, 31.524416602558681195 The (conditoned) standard-deviation of duration is, 20.892419502536867669 The (conditioned) correlation between them is, 0.9956440631 ---------------------------------------------------- if the prob. of getting a Heads is, 3/10, then -5 The prob. of finishing is, 0.6842435516 10 The (conditoned) expected duration is, 18.414912364353342070 The (conditoned) standard-deviation of duration is, 12.045046239592758081 The (conditoned) expected distance traveled is, 31.305343560337389626 The (conditoned) standard-deviation of duration is, 20.603215668310905016 The (conditioned) correlation between them is, 0.9954358181 ---------------------------------------------------- 31 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.6470837262 10 The (conditoned) expected duration is, 18.397759299187664684 The (conditoned) standard-deviation of duration is, 11.952361219623874768 The (conditoned) expected distance traveled is, 31.092204771857298394 The (conditoned) standard-deviation of duration is, 20.324592672788481464 The (conditioned) correlation between them is, 0.9952262897 ---------------------------------------------------- if the prob. of getting a Heads is, 8/25, then -5 The prob. of finishing is, 0.6045516222 10 The (conditoned) expected duration is, 18.383381219091689111 The (conditoned) standard-deviation of duration is, 11.863796261248414247 The (conditoned) expected distance traveled is, 30.884070510549644722 The (conditoned) standard-deviation of duration is, 20.055237109878937240 The (conditioned) correlation between them is, 0.9950154846 ---------------------------------------------------- 33 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.5560884078 10 The (conditoned) expected duration is, 18.371358087903750454 The (conditoned) standard-deviation of duration is, 11.778736287333774983 The (conditoned) expected distance traveled is, 30.680156758025042764 The (conditoned) standard-deviation of duration is, 19.793942449321006937 The (conditioned) correlation between them is, 0.9948033626 ---------------------------------------------------- 17 if the prob. of getting a Heads is, --, then 50 -5 The prob. of finishing is, 0.5038496252 10 The (conditoned) expected duration is, 18.361332696394676484 The (conditoned) standard-deviation of duration is, 11.696603499934726310 The (conditoned) expected distance traveled is, 30.479800387261280701 The (conditoned) standard-deviation of duration is, 19.539593616794279501 The (conditioned) correlation between them is, 0.9945898346 ---------------------------------------------------- if the prob. of getting a Heads is, 7/20, then -5 The prob. of finishing is, 0.4514312769 10 The (conditoned) expected duration is, 18.353001583163751901 The (conditoned) standard-deviation of duration is, 11.616862405937445284 The (conditoned) expected distance traveled is, 30.282440960735323671 The (conditoned) standard-deviation of duration is, 19.291171116542309725 The (conditioned) correlation between them is, 0.9943747728 ---------------------------------------------------- if the prob. of getting a Heads is, 9/25, then -5 The prob. of finishing is, 0.4025848968 10 The (conditoned) expected duration is, 18.346108024039348317 The (conditoned) standard-deviation of duration is, 11.539028031390843609 The (conditoned) expected distance traveled is, 30.087606565667871083 The (conditoned) standard-deviation of duration is, 19.047761650956912669 The (conditioned) correlation between them is, 0.9941580257 ---------------------------------------------------- 37 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.3602425547 10 The (conditoned) expected duration is, 18.340436115361770929 The (conditoned) standard-deviation of duration is, 11.462672192216922787 The (conditoned) expected distance traveled is, 29.894901906630533439 The (conditoned) standard-deviation of duration is, 18.808566047810449646 The (conditioned) correlation between them is, 0.9939394326 ---------------------------------------------------- 19 if the prob. of getting a Heads is, --, then 50 -5 The prob. of finishing is, 0.3259513668 10 The (conditoned) expected duration is, 18.335805457300696340 The (conditoned) standard-deviation of duration is, 11.387425751372296321 The (conditoned) expected distance traveled is, 29.703997739052021857 The (conditoned) standard-deviation of duration is, 18.572900688441204013 The (conditioned) correlation between them is, 0.9937188371 ---------------------------------------------------- 39 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.2996975330 10 The (conditoned) expected duration is, 18.332066222930765600 The (conditoned) standard-deviation of duration is, 11.312976561145833629 The (conditoned) expected distance traveled is, 29.514621240803135864 The (conditoned) standard-deviation of duration is, 18.340191976939437294 The (conditioned) correlation between them is, 0.9934960956 ---------------------------------------------------- if the prob. of getting a Heads is, 2/5, then -5 The prob. of finishing is, 0.2800755375 10 The (conditoned) expected duration is, 18.329094492236179307 The (conditoned) standard-deviation of duration is, 11.239063239460476477 The (conditoned) expected distance traveled is, 29.326547098380855271 The (conditoned) standard-deviation of duration is, 18.109964336056564312 The (conditioned) correlation between them is, 0.9932710822 ---------------------------------------------------- 41 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.2647473261 10 The (conditoned) expected duration is, 18.326787788797451071 The (conditoned) standard-deviation of duration is, 11.165465174689396075 The (conditoned) expected distance traveled is, 29.139589181278514986 The (conditoned) standard-deviation of duration is, 17.881822507756945225 The (conditioned) correlation between them is, 0.9930436869 ---------------------------------------------------- 21 if the prob. of getting a Heads is, --, then 50 -5 The prob. of finishing is, 0.2510860539 10 The (conditoned) expected duration is, 18.325060879745620177 The (conditoned) standard-deviation of duration is, 11.091989983515496140 The (conditoned) expected distance traveled is, 28.953592867273880489 The (conditoned) standard-deviation of duration is, 17.655430035578639853 The (conditioned) correlation between them is, 0.9928138079 ---------------------------------------------------- 43 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.2368319239 10 The (conditoned) expected duration is, 18.323842047663602110 The (conditoned) standard-deviation of duration is, 11.018460774574952739 The (conditoned) expected distance traveled is, 28.768428312045694566 The (conditoned) standard-deviation of duration is, 17.430487485815047035 The (conditioned) correlation between them is, 0.9925813390 ---------------------------------------------------- 11 if the prob. of getting a Heads is, --, then 25 -5 The prob. of finishing is, 0.2205677417 10 The (conditoned) expected duration is, 18.323070100804594547 The (conditoned) standard-deviation of duration is, 10.944706050348082689 The (conditoned) expected distance traveled is, 28.583985048629966635 The (conditoned) standard-deviation of duration is, 17.206714801711446268 The (conditioned) correlation between them is, 0.9923461565 ---------------------------------------------------- if the prob. of getting a Heads is, 9/20, then -5 The prob. of finishing is, 0.2018867152 10 The (conditoned) expected duration is, 18.322692286919498149 The (conditoned) standard-deviation of duration is, 10.870554285717951916 The (conditoned) expected distance traveled is, 28.400168145957076027 The (conditoned) standard-deviation of duration is, 16.983841096437944492 The (conditioned) correlation between them is, 0.9921081113 ---------------------------------------------------- 23 if the prob. of getting a Heads is, --, then 50 -5 The prob. of finishing is, 0.1812489756 10 The (conditoned) expected duration is, 18.322663063012080548 The (conditoned) standard-deviation of duration is, 10.795833451722381894 The (conditoned) expected distance traveled is, 28.216895823166805229 The (conditoned) standard-deviation of duration is, 16.761602497376539134 The (conditioned) correlation between them is, 0.9918670261 ---------------------------------------------------- 47 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.1596381947 10 The (conditoned) expected duration is, 18.322943473069734460 The (conditoned) standard-deviation of duration is, 10.720373990303009108 The (conditoned) expected distance traveled is, 28.034098103967788373 The (conditoned) standard-deviation of duration is, 16.539745833393893063 The (conditioned) correlation between them is, 0.9916226998 ---------------------------------------------------- 12 if the prob. of getting a Heads is, --, then 25 -5 The prob. of finishing is, 0.1381776362 10 The (conditoned) expected duration is, 18.323500804823943263 The (conditoned) standard-deviation of duration is, 10.644012899139165905 The (conditoned) expected distance traveled is, 27.851715971778541798 The (conditoned) standard-deviation of duration is, 16.318034485349036300 The (conditioned) correlation between them is, 0.9913749146 ---------------------------------------------------- 49 if the prob. of getting a Heads is, ---, then 100 -5 The prob. of finishing is, 0.1178355675 10 The (conditoned) expected duration is, 18.324308255229031437 The (conditoned) standard-deviation of duration is, 10.566596895568566022 The (conditoned) expected distance traveled is, 27.669700584008775256 The (conditoned) standard-deviation of duration is, 16.096253080608366482 The (conditioned) correlation between them is, 0.9911234427 ---------------------------------------------------- if the prob. of getting a Heads is, 1/2, then -6 The prob. of finishing is, 0.9927701001 10 The (conditoned) expected duration is, 18.325344471934522952 The (conditoned) standard-deviation of duration is, 10.487983653675273362 The (conditoned) expected distance traveled is, 27.488012326092181353 The (conditoned) standard-deviation of duration is, 15.874209283102535937 The (conditioned) correlation between them is, 0.9908680506 ---------------------------------------------------- 51 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.8284891196 10 The (conditoned) expected duration is, 18.326592970004671462 The (conditoned) standard-deviation of duration is, 10.408041163370658812 The (conditoned) expected distance traveled is, 27.306619698201319990 The (conditoned) standard-deviation of duration is, 15.651732633246646760 The (conditioned) correlation between them is, 0.9906085000 ---------------------------------------------------- 13 if the prob. of getting a Heads is, --, then 25 -6 The prob. of finishing is, 0.6864814414 10 The (conditoned) expected duration is, 18.328041496257027238 The (conditoned) standard-deviation of duration is, 10.326645877833490482 The (conditoned) expected distance traveled is, 27.125498145224800369 The (conditoned) standard-deviation of duration is, 15.428671441619538515 The (conditioned) correlation between them is, 0.9903445462 ---------------------------------------------------- 53 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.5661842646 10 The (conditoned) expected duration is, 18.329681423521710591 The (conditoned) standard-deviation of duration is, 10.243680422838440937 The (conditoned) expected distance traveled is, 26.944628956763110305 The (conditoned) standard-deviation of duration is, 15.204888968183725067 The (conditioned) correlation between them is, 0.9900759356 ---------------------------------------------------- 27 if the prob. of getting a Heads is, --, then 50 -6 The prob. of finishing is, 0.4663840219 10 The (conditoned) expected duration is, 18.331507230994863706 The (conditoned) standard-deviation of duration is, 10.159031439144203263 The (conditoned) expected distance traveled is, 26.763998321965976552 The (conditoned) standard-deviation of duration is, 14.980259817452268319 The (conditioned) correlation between them is, 0.9898024022 ---------------------------------------------------- 11 if the prob. of getting a Heads is, --, then 20 -6 The prob. of finishing is, 0.3858181575 10 The (conditoned) expected duration is, 18.333516095202756109 The (conditoned) standard-deviation of duration is, 10.072587866012892025 The (conditoned) expected distance traveled is, 26.583596572912675750 The (conditoned) standard-deviation of duration is, 14.754667049296327006 The (conditioned) correlation between them is, 0.9895236645 ---------------------------------------------------- 14 if the prob. of getting a Heads is, --, then 25 -6 The prob. of finishing is, 0.3234336528 10 The (conditoned) expected duration is, 18.335707595006173415 The (conditoned) standard-deviation of duration is, 9.9842397903441420045 The (conditoned) expected distance traveled is, 26.403417616144504368 The (conditoned) standard-deviation of duration is, 14.528000190783710933 The (conditioned) correlation between them is, 0.9892394227 ---------------------------------------------------- 57 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.2783058919 10 The (conditoned) expected duration is, 18.338083523174644729 The (conditoned) standard-deviation of duration is, 9.8938778843020889334 The (conditoned) expected distance traveled is, 26.223458535167467884 The (conditoned) standard-deviation of duration is, 14.300154165297686031 The (conditioned) correlation between them is, 0.9889493575 ---------------------------------------------------- 29 if the prob. of getting a Heads is, --, then 50 -6 The prob. of finishing is, 0.2492789705 10 The (conditoned) expected duration is, 18.340647787728072725 The (conditoned) standard-deviation of duration is, 9.8013933612444334296 The (conditoned) expected distance traveled is, 26.043719334362673391 The (conditoned) standard-deviation of duration is, 14.071029028779087485 The (conditioned) correlation between them is, 0.9886531290 ---------------------------------------------------- 59 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.2344699862 10 The (conditoned) expected duration is, 18.343406372271356868 The (conditoned) standard-deviation of duration is, 9.7066782366824239056 The (conditoned) expected distance traveled is, 25.864202776886945942 The (conditoned) standard-deviation of duration is, 13.840530221529402978 The (conditioned) correlation between them is, 0.9883503771 ---------------------------------------------------- if the prob. of getting a Heads is, 3/5, then -6 The prob. of finishing is, 0.2308679147 10 The (conditoned) expected duration is, 18.346367309111950445 The (conditoned) standard-deviation of duration is, 9.6096255114657157815 The (conditoned) expected distance traveled is, 25.684914249303799218 The (conditoned) standard-deviation of duration is, 13.608568819202767238 The (conditioned) correlation between them is, 0.9880407221 ---------------------------------------------------- 61 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.2342867962 10 The (conditoned) expected duration is, 18.349540614076702787 The (conditoned) standard-deviation of duration is, 9.5101288089363928074 The (conditoned) expected distance traveled is, 25.505861580059363934 The (conditoned) standard-deviation of duration is, 13.375061137357529407 The (conditioned) correlation between them is, 0.9877237640 ---------------------------------------------------- 31 if the prob. of getting a Heads is, --, then 50 -6 The prob. of finishing is, 0.2398369909 10 The (conditoned) expected duration is, 18.352938149831380347 The (conditoned) standard-deviation of duration is, 9.4080811220712416708 The (conditoned) expected distance traveled is, 25.327054764264072323 The (conditoned) standard-deviation of duration is, 13.139927186161387839 The (conditioned) correlation between them is, 0.9873990799 ---------------------------------------------------- 63 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.2428561779 10 The (conditoned) expected duration is, 18.356573425516646445 The (conditoned) standard-deviation of duration is, 9.3033726876427438545 The (conditoned) expected distance traveled is, 25.148505604100813784 The (conditoned) standard-deviation of duration is, 12.903087941975758333 The (conditioned) correlation between them is, 0.9870662171 ---------------------------------------------------- 16 if the prob. of getting a Heads is, --, then 25 -6 The prob. of finishing is, 0.2399890443 10 The (conditoned) expected duration is, 18.360461387340919000 The (conditoned) standard-deviation of duration is, 9.1958884606022073157 The (conditoned) expected distance traveled is, 24.970227338739610116 The (conditoned) standard-deviation of duration is, 12.664462028795594752 The (conditioned) correlation between them is, 0.9867246840 ---------------------------------------------------- 13 if the prob. of getting a Heads is, --, then 20 -6 The prob. of finishing is, 0.2299702182 10 The (conditoned) expected duration is, 18.364618280186097396 The (conditoned) standard-deviation of duration is, 9.0855059560318985315 The (conditoned) expected distance traveled is, 24.792234372427974152 The (conditoned) standard-deviation of duration is, 12.423962839186112543 The (conditioned) correlation between them is, 0.9863739397 ---------------------------------------------------- 33 if the prob. of getting a Heads is, --, then 50 -6 The prob. of finishing is, 0.2137510714 10 The (conditoned) expected duration is, 18.369061645434720063 The (conditoned) standard-deviation of duration is, 8.9720941507046278309 The (conditoned) expected distance traveled is, 24.614542188631359058 The (conditoned) standard-deviation of duration is, 12.181497070199043135 The (conditioned) correlation between them is, 0.9860133856 ---------------------------------------------------- 67 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.1938909112 10 The (conditoned) expected duration is, 18.373810469709741666 The (conditoned) standard-deviation of duration is, 8.8555136922424691026 The (conditoned) expected distance traveled is, 24.437167468383931716 The (conditoned) standard-deviation of duration is, 11.936965076601412543 The (conditioned) correlation between them is, 0.9856423602 ---------------------------------------------------- 17 if the prob. of getting a Heads is, --, then 25 -6 The prob. of finishing is, 0.1734598306 10 The (conditoned) expected duration is, 18.378885439690912515 The (conditoned) standard-deviation of duration is, 8.7356180763373651866 The (conditoned) expected distance traveled is, 24.260128349485695412 The (conditoned) standard-deviation of duration is, 11.690262641690592243 The (conditioned) correlation between them is, 0.9852601371 ---------------------------------------------------- 69 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.1549030843 10 The (conditoned) expected duration is, 18.384309220914918887 The (conditoned) standard-deviation of duration is, 8.6122550255512828630 The (conditoned) expected distance traveled is, 24.083444713018411227 The (conditoned) standard-deviation of duration is, 11.441283156210951098 The (conditioned) correlation between them is, 0.9848659253 ---------------------------------------------------- if the prob. of getting a Heads is, 7/10, then -6 The prob. of finishing is, 0.1393051330 10 The (conditoned) expected duration is, 18.390106680190250323 The (conditoned) standard-deviation of duration is, 8.4852672324177429026 The (conditoned) expected distance traveled is, 23.907138387335032518 The (conditoned) standard-deviation of duration is, 11.189919065202971676 The (conditioned) correlation between them is, 0.9844588675 ---------------------------------------------------- 71 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.1262920611 10 The (conditoned) expected duration is, 18.396305007411938863 The (conditoned) standard-deviation of duration is, 8.3544919152481724704 The (conditoned) expected distance traveled is, 23.731233209919328040 The (conditoned) standard-deviation of duration is, 10.936061806017605736 The (conditioned) correlation between them is, 0.9840380345 ---------------------------------------------------- 18 if the prob. of getting a Heads is, --, then 25 -6 The prob. of finishing is, 0.1145286980 10 The (conditoned) expected duration is, 18.402933744217529145 The (conditoned) standard-deviation of duration is, 8.2197591250326558100 The (conditoned) expected distance traveled is, 23.555754957460244594 The (conditoned) standard-deviation of duration is, 10.679600113247956070 The (conditioned) correlation between them is, 0.9836024148 ---------------------------------------------------- 73 if the prob. of getting a Heads is, ---, then 100 -6 The prob. of finishing is, 0.1025246604 10 The (conditoned) expected duration is, 18.410024771616835725 The (conditoned) standard-deviation of duration is, 8.0808892227612180212 The (conditoned) expected distance traveled is, 23.380731213509459501 The (conditoned) standard-deviation of duration is, 10.420417217447380042 The (conditioned) correlation between them is, 0.9831508975 ---------------------------------------------------- 37 if the prob. of getting a Heads is, --, then 50 -7 The prob. of finishing is, 0.8936113273 10 The (conditoned) expected duration is, 18.417612328159811771 The (conditoned) standard-deviation of duration is, 7.9376902154382933187 The (conditoned) expected distance traveled is, 23.206191267544329492 The (conditoned) standard-deviation of duration is, 10.158387844069125341 The (conditioned) correlation between them is, 0.9826822532 ---------------------------------------------------- if the prob. of getting a Heads is, 3/4, then -7 The prob. of finishing is, 0.7503141185 10 The (conditoned) expected duration is, 18.425733116124257364 The (conditoned) standard-deviation of duration is, 7.7899555682820739397 The (conditoned) expected distance traveled is, 23.032166119531843673 The (conditoned) standard-deviation of duration is, 9.8933758574430576295 The (conditioned) correlation between them is, 0.9821951123 ---------------------------------------------------- 19 if the prob. of getting a Heads is, --, then 25 -7 The prob. of finishing is, 0.6031141739 10 The (conditoned) expected duration is, 18.434426512975910933 The (conditoned) standard-deviation of duration is, 7.6374627254160519045 The (conditoned) expected distance traveled is, 22.858688610780072973 The (conditoned) standard-deviation of duration is, 9.6252329144049263521 The (conditioned) correlation between them is, 0.9816879459 ---------------------------------------------------- 77 if the prob. of getting a Heads is, ---, then 100 -7 The prob. of finishing is, 0.4631728867 10 The (conditoned) expected duration is, 18.443734861533176896 The (conditoned) standard-deviation of duration is, 7.4799720785824344626 The (conditoned) expected distance traveled is, 22.685793644591190142 The (conditoned) standard-deviation of duration is, 9.3537978494491787018 The (conditioned) correlation between them is, 0.9811590454 ---------------------------------------------------- 39 if the prob. of getting a Heads is, --, then 50 -7 The prob. of finishing is, 0.3402766926 10 The (conditoned) expected duration is, 18.453703790166268163 The (conditoned) standard-deviation of duration is, 7.3172258051033809783 The (conditoned) expected distance traveled is, 22.513518431601386396 The (conditoned) standard-deviation of duration is, 9.0788960753117939366 The (conditioned) correlation between them is, 0.9806065013 ---------------------------------------------------- 79 if the prob. of getting a Heads is, ---, then 100 -7 The prob. of finishing is, 0.2399424727 10 The (conditoned) expected duration is, 18.464382524085674726 The (conditoned) standard-deviation of duration is, 7.1489460096924389725 The (conditoned) expected distance traveled is, 22.341902707441628169 The (conditoned) standard-deviation of duration is, 8.8003382738530474787 The (conditioned) correlation between them is, 0.9800281767 ---------------------------------------------------- if the prob. of getting a Heads is, 4/5, then -7 The prob. of finishing is, 0.1630337210 10 The (conditoned) expected duration is, 18.475824178197619527 The (conditoned) standard-deviation of duration is, 6.9748318645914826497 The (conditoned) expected distance traveled is, 22.170988908506734123 The (conditoned) standard-deviation of duration is, 8.5179179844493245948 The (conditioned) correlation between them is, 0.9794216731 ---------------------------------------------------- 81 if the prob. of getting a Heads is, ---, then 100 -7 The prob. of finishing is, 0.1070898219 10 The (conditoned) expected duration is, 18.488086048420294501 The (conditoned) standard-deviation of duration is, 6.7945557086395267188 The (conditoned) expected distance traveled is, 22.000822325677625776 The (conditoned) standard-deviation of duration is, 8.2314080647134144075 The (conditioned) correlation between them is, 0.9787842875 ---------------------------------------------------- 41 if the prob. of getting a Heads is, --, then 50 -8 The prob. of finishing is, 0.6811071046 10 The (conditoned) expected duration is, 18.501229927358087944 The (conditoned) standard-deviation of duration is, 6.6077581477654968838 The (conditoned) expected distance traveled is, 21.831451267171527758 The (conditoned) standard-deviation of duration is, 7.9405561410513970712 The (conditioned) correlation between them is, 0.9781129596 ---------------------------------------------------- 83 if the prob. of getting a Heads is, ---, then 100 -8 The prob. of finishing is, 0.4192860335 10 The (conditoned) expected duration is, 18.515322463780675846 The (conditoned) standard-deviation of duration is, 6.4140420765795551850 The (conditoned) expected distance traveled is, 21.662927252918856280 The (conditoned) standard-deviation of duration is, 7.6450790433484408782 The (conditioned) correlation between them is, 0.9774042087 ---------------------------------------------------- 21 if the prob. of getting a Heads is, --, then 25 -8 The prob. of finishing is, 0.2492606372 10 The (conditoned) expected duration is, 18.530435574506972127 The (conditoned) standard-deviation of duration is, 6.2129653100906190815 The (conditoned) expected distance traveled is, 21.495305248382859585 The (conditoned) standard-deviation of duration is, 7.3446559537101572979 The (conditioned) correlation between them is, 0.9766540572 ---------------------------------------------------- 17 if the prob. of getting a Heads is, --, then 20 -8 The prob. of finishing is, 0.1425573280 10 The (conditoned) expected duration is, 18.546646910630191520 The (conditoned) standard-deviation of duration is, 6.0040312600820153416 The (conditoned) expected distance traveled is, 21.328643936687771113 The (conditoned) standard-deviation of duration is, 7.0389197148385220334 The (conditioned) correlation between them is, 0.9758579383 ---------------------------------------------------- 43 if the prob. of getting a Heads is, --, then 50 -9 The prob. of finishing is, 0.7803281490 10 The (conditoned) expected duration is, 18.564040379038274267 The (conditoned) standard-deviation of duration is, 5.7866768095971917930 The (conditoned) expected distance traveled is, 21.163006026216656124 The (conditoned) standard-deviation of duration is, 6.7274454527857894405 The (conditioned) correlation between them is, 0.9750105825 ---------------------------------------------------- 87 if the prob. of getting a Heads is, ---, then 100 -9 The prob. of finishing is, 0.4061452752 10 The (conditoned) expected duration is, 18.582706722212304136 The (conditoned) standard-deviation of duration is, 5.5602561515221859084 The (conditoned) expected distance traveled is, 20.998458592972816686 The (conditoned) standard-deviation of duration is, 6.4097352870882291585 The (conditioned) correlation between them is, 0.9741058769 ---------------------------------------------------- 22 if the prob. of getting a Heads is, --, then 25 -9 The prob. of finishing is, 0.1993673263 10 The (conditoned) expected duration is, 18.602744161727996595 The (conditoned) standard-deviation of duration is, 5.3240187343329775947 The (conditoned) expected distance traveled is, 20.835073459568854752 The (conditoned) standard-deviation of duration is, 6.0851972895425660118 The (conditioned) correlation between them is, 0.9731366909 ---------------------------------------------------- 89 if the prob. of getting a Heads is, ---, then 100 -10 The prob. of finishing is, 0.9135054356 10 The (conditoned) expected duration is, 18.624259112791167980 The (conditoned) standard-deviation of duration is, 5.0770784049465243717 The (conditoned) expected distance traveled is, 20.672927614465732961 The (conditoned) standard-deviation of duration is, 5.7531158110252179044 The (conditioned) correlation between them is, 0.9720946547 ---------------------------------------------------- if the prob. of getting a Heads is, 9/10, then -10 The prob. of finishing is, 0.3855510389 10 The (conditoned) expected duration is, 18.647366978621839171 The (conditoned) standard-deviation of duration is, 4.8183690091175924236 The (conditoned) expected distance traveled is, 20.512103676168568742 The (conditoned) standard-deviation of duration is, 5.4126084769808185286 The (conditioned) correlation between them is, 0.9709698793 ---------------------------------------------------- 91 if the prob. of getting a Heads is, ---, then 100 -10 The prob. of finishing is, 0.1472872877 10 The (conditoned) expected duration is, 18.672193034891739585 The (conditoned) standard-deviation of duration is, 4.5465784154506670589 The (conditoned) expected distance traveled is, 20.352690407909030736 The (conditoned) standard-deviation of duration is, 5.0625618681656683878 The (conditioned) correlation between them is, 0.9697505962 ---------------------------------------------------- 23 if the prob. of getting a Heads is, --, then 25 -11 The prob. of finishing is, 0.4973534906 10 The (conditoned) expected duration is, 18.698873415924041499 The (conditoned) standard-deviation of duration is, 4.2600467090257756691 The (conditoned) expected distance traveled is, 20.194783289155597522 The (conditoned) standard-deviation of duration is, 4.7015316897989170567 The (conditioned) correlation between them is, 0.9684226901 ---------------------------------------------------- 93 if the prob. of getting a Heads is, ---, then 100 -11 The prob. of finishing is, 0.1435965767 10 The (conditoned) expected duration is, 18.727556216077626103 The (conditoned) standard-deviation of duration is, 3.9566018486760822218 The (conditoned) expected distance traveled is, 20.038485151190579086 The (conditoned) standard-deviation of duration is, 4.3275807688881338729 The (conditioned) correlation between them is, 0.9669690846 ---------------------------------------------------- 47 if the prob. of getting a Heads is, --, then 50 -12 The prob. of finishing is, 0.3376404946 10 The (conditoned) expected duration is, 18.758402721714091493 The (conditoned) standard-deviation of duration is, 3.6332792938510978749 The (conditoned) expected distance traveled is, 19.883906885013942810 The (conditoned) standard-deviation of duration is, 3.9380013522504618764 The (conditioned) correlation between them is, 0.9653689253 ---------------------------------------------------- 19 if the prob. of getting a Heads is, --, then 20 -13 The prob. of finishing is, 0.5995250368 10 The (conditoned) expected duration is, 18.791588791431486572 The (conditoned) standard-deviation of duration is, 3.2858090164682434613 The (conditoned) expected distance traveled is, 19.731168231002518480 The (conditoned) standard-deviation of duration is, 3.5288047668652759133 The (conditioned) correlation between them is, 0.9635964769 ---------------------------------------------------- 24 if the prob. of getting a Heads is, --, then 25 -14 The prob. of finishing is, 0.7083805191 10 The (conditoned) expected duration is, 18.827306404897832143 The (conditoned) standard-deviation of duration is, 2.9075861189209271934 The (conditoned) expected distance traveled is, 19.580398661093680039 The (conditoned) standard-deviation of duration is, 3.0936930878524444704 The (conditioned) correlation between them is, 0.9616196104 ---------------------------------------------------- 97 if the prob. of getting a Heads is, ---, then 100 -15 The prob. of finishing is, 0.4393800372 10 The (conditoned) expected duration is, 18.865765403692728462 The (conditoned) standard-deviation of duration is, 2.4873203522872207946 The (conditoned) expected distance traveled is, 19.431738365803506180 The (conditoned) standard-deviation of duration is, 2.6217014899226439372 The (conditioned) correlation between them is, 0.9593976910 ---------------------------------------------------- 49 if the prob. of getting a Heads is, --, then 50 -17 The prob. of finishing is, 0.8400366644 10 The (conditoned) expected duration is, 18.907195451140950891 The (conditoned) standard-deviation of duration is, 2.0024939207287856458 The (conditoned) expected distance traveled is, 19.285339360163769828 The (conditoned) standard-deviation of duration is, 2.0906087487494942032 The (conditioned) correlation between them is, 0.9568785717 ---------------------------------------------------- 99 if the prob. of getting a Heads is, ---, then 100 -20 The prob. of finishing is, 0.9052869549 10 The (conditoned) expected duration is, 18.951848242285327964 The (conditoned) standard-deviation of duration is, 1.3932435901344098953 The (conditoned) expected distance traveled is, 19.141366724708181246 The (conditoned) standard-deviation of duration is, 1.4405099168908979434 The (conditioned) correlation between them is, 0.9539942144 ---------------------------------- This took , 18.588, seconds.