#Ok to post homework #Tifany Tong, November 8th, 2020, HW #17a # Question 1 # GFv(USEC(), x) = x^538 + 8*x^535 + 5*x^534 + 3*x^533 + 34*x^532 + 43*x^531 + 36*x^530 + 122*x^529 + 201*x^528 + 217*x^527 + 427*x^526 + 730*x^525 + 920*x^524 + 1434*x^523 + 2330*x^522 + 3162*x^521 + 4508*x^520 + 6821*x^519 + 9479*x^518 + 13080*x^517 + 18682*x^516 + 25832*x^515 + 35065*x^514 + 48207*x^513 + 65508*x^512 + 87739*x^511 + 117572*x^510 + 156685*x^509 + 206935*x^508 + 272173*x^507 + 356345*x^506 + 463822*x^505 + 600849*x^504 + 774662*x^503 + 994337*x^502 + 1270768*x^501 + 1616541*x^500 + 2048369*x^499 + 2585598*x^498 + 3249925*x^497 + 4069867*x^496 + 5079078*x^495 + 6314467*x^494 + 7823149*x^493 + 9661071*x^492 + 11890042*x^491 + 14586067*x^490 + 17839141*x^489 + 21749899*x^488 + 26438475*x^487 + 32046021*x^486 + 38731301*x^485 + 46681006*x^484 + 56111173*x^483 + 67265736*x^482 + 80428483*x^481 + 95923935*x^480 + 114117746*x^479 + 135431808*x^478 + 160344810*x^477 + 189392667*x^476 + 223189856*x^475 + 262428980*x^474 + 307880930*x^473 + 360421915*x^472 + 421035657*x^471 + 490811551*x^470 + 5709757# 86*x^469 + 662899405*x^468 + 768094894*x^467 + 888249964*x^466 + 1025240398*x^465 + 1181130618*x^464 + 1358206138*x^463 + 1558990312*x^462 + 1786252409*x^461 + 2043040165*x^460 + 2332695429*x^459 + 2658870568*x^458 + 3025567470*x^457 + 3437146528*x^456 + 3898350489*x^455 + 4414352627*x^454 + 4990760988*x^453 + 5633643424*x^452 + 6349587741*x^451 + 7145704429*x^450 + 8029647723*x^449 + 9009686538*x^448 + 10094708495*x^447 + 11294238537*x^446 + 12618513241*x^445 + 14078488658*x^444 + 15685857870*x^443 + 17453125685*x^442 + 19393617918*x^441 + 21521499793*x^440 + 23851849790*x^439 + 26400664613*x^438 + 29184882177*x^437 + 32222453648*x^436 + 35532339797*x^435 + 39134535973*x^434 + 43050144947*x^433 + 47301362511*x^432 + 51911499571*x^431 + 56905057539*x^430 + 62307700923*x^429 + 68146273105*x^428 + 74448872844*x^427 + 81244816938*x^426 + 88564644621*x^425 + 96440188453*x^424 + 104904532333*x^423 + 113992004741*x^422 + 123738237027*x^421 + 134180113015*x^420 + 145355758292*x^419 + 157304580196*x^418 + 170067202# 350*x^417 + 183685457590*x^416 + 198202408042*x^415 + 213662255583*x^414 + 230110337445*x^413 + 247593139583*x^412 + 266158172954*x^411 + 285853963718*x^410 + 306730068064*x^409 + 328836918688*x^408 + 352225800892*x^407 + 376948865953*x^406 + 403058961273*x^405 + 430609581706*x^404 + 459654879646*x^403 + 490249486728*x^402 + 522448446323*x^401 + 556307206020*x^400 + 591881433527*x^399 + 629226945869*x^398 + 668399676139*x^397 + 709455482123*x^396 + 752450074576*x^395 + 797438967890*x^394 + 844477271443*x^393 + 893619626284*x^392 + 944920144061*x^391 + 998432176367*x^390 + 1054208260428*x^389 + 1112300053668*x^388 + 1172758090898*x^387 + 1235631725736*x^386 + 1300969070333*x^385 + 1368816743171*x^384 + 1439219811592*x^383 + 1512221733293*x^382 + 1587864104004*x^381 + 1666186601756*x^380 + 1747226922544*x^379 + 1831020544692*x^378 + 1917600677723*x^377 + 2006998189890*x^376 + 2099241380376*x^375 + 2194355954575*x^374 + 2292364942448*x^373 + 2393288472556*x^372 + 2497143781269*x^371 + 2603945128309*x^370 + 271# 3703569031*x^369 + 2826426993933*x^368 + 2942120066210*x^367 + 3060783981004*x^366 + 3182416524832*x^365 + 3307012046945*x^364 + 3434561225645*x^363 + 3565051131004*x^362 + 3698465221563*x^361 + 3834783141606*x^360 + 3973980781619*x^359 + 4116030292397*x^358 + 4260899922648*x^357 + 4408554089850*x^356 + 4558953388854*x^355 + 4712054472792*x^354 + 4867810158974*x^353 + 5026169423561*x^352 + 5187077307934*x^351 + 5350475067160*x^350 + 5516300169293*x^349 + 5684486211266*x^348 + 5854963107251*x^347 + 6027657103282*x^346 + 6202490695643*x^345 + 6379382850728*x^344 + 6558249046909*x^343 + 6739001203352*x^342 + 6921547906574*x^341 + 7105794480365*x^340 + 7291642941851*x^339 + 7478992230098*x^338 + 7667738290388*x^337 + 7857774059618*x^336 + 8048989703546*x^335 + 8241272700785*x^334 + 8434507865623*x^333 + 8628577597686*x^332 + 8823361952383*x^331 + 9018738688916*x^330 + 9214583548036*x^329 + 9410770317986*x^328 + 9607170879264*x^327 + 9803655512445*x^326 + 10000092968338*x^325 + 10196350507747*x^324 + 10392294222# 573*x^323 + 10587789125958*x^322 + 10782699181774*x^321 + 10976887613498*x^320 + 11170217031674*x^319 + 11362549466188*x^318 + 11553746646010*x^317 + 11743670135244*x^316 + 11932181400862*x^315 + 12119142062779*x^314 + 12304414017695*x^313 + 12487859542917*x^312 + 12669341528675*x^311 + 12848723576633*x^310 + 13025870124994*x^309 + 13200646697126*x^308 + 13372919957601*x^307 + 13542557836144*x^306 + 13709429797337*x^305 + 13873406885786*x^304 + 14034361825186*x^303 + 14192169290107*x^302 + 14346705962992*x^301 + 14497850601898*x^300 + 14645484307520*x^299 + 14789490592886*x^298 + 14929755436539*x^297 + 15066167512346*x^296 + 15198618276161*x^295 + 15327002026946*x^294 + 15451216094853*x^293 + 15571160921779*x^292 + 15686740130226*x^291 + 15797860694803*x^290 + 15904432998027*x^289 + 16006370908045*x^288 + 16103591935405*x^287 + 16196017263096*x^286 + 16283571817344*x^285 + 16366184428318*x^284 + 16443787845527*x^283 + 16516318770336*x^282 + 16583718019998*x^281 + 16645930548169*x^280 + 16702905445106*x^279 # + 16754596077474*x^278 + 16800960124978*x^277 + 16841959555260*x^276 + 16877560724971*x^275 + 16907734437204*x^274 + 16932455907218*x^273 + 16951704812511*x^272 + 16965465344318*x^271 + 16973726193241*x^270 + 16976480564070*x^269 + 16973726193241*x^268 + 16965465344318*x^267 + 16951704812511*x^266 + 16932455907218*x^265 + 16907734437204*x^264 + 16877560724971*x^263 + 16841959555260*x^262 + 16800960124978*x^261 + 16754596077474*x^260 + 16702905445106*x^259 + 16645930548169*x^258 + 16583718019998*x^257 + 16516318770336*x^256 + 16443787845527*x^255 + 16366184428318*x^254 + 16283571817344*x^253 + 16196017263096*x^252 + 16103591935405*x^251 + 16006370908045*x^250 + 15904432998027*x^249 + 15797860694803*x^248 + 15686740130226*x^247 + 15571160921779*x^246 + 15451216094853*x^245 + 15327002026946*x^244 + 15198618276161*x^243 + 15066167512346*x^242 + 14929755436539*x^241 + 14789490592886*x^240 + 14645484307520*x^239 + 14497850601898*x^238 + 14346705962992*x^237 + 14192169290107*x^236 + 14034361825186*x^235 + 13873406# 885786*x^234 + 13709429797337*x^233 + 13542557836144*x^232 + 13372919957601*x^231 + 13200646697126*x^230 + 13025870124994*x^229 + 12848723576633*x^228 + 12669341528675*x^227 + 12487859542917*x^226 + 12304414017695*x^225 + 12119142062779*x^224 + 11932181400862*x^223 + 11743670135244*x^222 + 11553746646010*x^221 + 11362549466188*x^220 + 11170217031674*x^219 + 10976887613498*x^218 + 10782699181774*x^217 + 10587789125958*x^216 + 10392294222573*x^215 + 10196350507747*x^214 + 10000092968338*x^213 + 9803655512445*x^212 + 9607170879264*x^211 + 9410770317986*x^210 + 9214583548036*x^209 + 9018738688916*x^208 + 8823361952383*x^207 + 8628577597686*x^206 + 8434507865623*x^205 + 8241272700785*x^204 + 8048989703546*x^203 + 7857774059618*x^202 + 7667738290388*x^201 + 7478992230098*x^200 + 7291642941851*x^199 + 7105794480365*x^198 + 6921547906574*x^197 + 6739001203352*x^196 + 6558249046909*x^195 + 6379382850728*x^194 + 6202490695643*x^193 + 6027657103282*x^192 + 5854963107251*x^191 + 5684486211266*x^190 + 5516300169293*x^18# 9 + 5350475067160*x^188 + 5187077307934*x^187 + 5026169423561*x^186 + 4867810158974*x^185 + 4712054472792*x^184 + 4558953388854*x^183 + 4408554089850*x^182 + 4260899922648*x^181 + 4116030292397*x^180 + 3973980781619*x^179 + 3834783141606*x^178 + 3698465221563*x^177 + 3565051131004*x^176 + 3434561225645*x^175 + 3307012046945*x^174 + 3182416524832*x^173 + 3060783981004*x^172 + 2942120066210*x^171 + 2826426993933*x^170 + 2713703569031*x^169 + 2603945128309*x^168 + 2497143781269*x^167 + 2393288472556*x^166 + 2292364942448*x^165 + 2194355954575*x^164 + 2099241380376*x^163 + 2006998189890*x^162 + 1917600677723*x^161 + 1831020544692*x^160 + 1747226922544*x^159 + 1666186601756*x^158 + 1587864104004*x^157 + 1512221733293*x^156 + 1439219811592*x^155 + 1368816743171*x^154 + 1300969070333*x^153 + 1235631725736*x^152 + 1172758090898*x^151 + 1112300053668*x^150 + 1054208260428*x^149 + 998432176367*x^148 + 944920144061*x^147 + 893619626284*x^146 + 844477271443*x^145 + 797438967890*x^144 + 752450074576*x^143 + 709455482123# *x^142 + 668399676139*x^141 + 629226945869*x^140 + 591881433527*x^139 + 556307206020*x^138 + 522448446323*x^137 + 490249486728*x^136 + 459654879646*x^135 + 430609581706*x^134 + 403058961273*x^133 + 376948865953*x^132 + 352225800892*x^131 + 328836918688*x^130 + 306730068064*x^129 + 285853963718*x^128 + 266158172954*x^127 + 247593139583*x^126 + 230110337445*x^125 + 213662255583*x^124 + 198202408042*x^123 + 183685457590*x^122 + 170067202350*x^121 + 157304580196*x^120 + 145355758292*x^119 + 134180113015*x^118 + 123738237027*x^117 + 113992004741*x^116 + 104904532333*x^115 + 96440188453*x^114 + 88564644621*x^113 + 81244816938*x^112 + 74448872844*x^111 + 68146273105*x^110 + 62307700923*x^109 + 56905057539*x^108 + 51911499571*x^107 + 47301362511*x^106 + 43050144947*x^105 + 39134535973*x^104 + 35532339797*x^103 + 32222453648*x^102 + 29184882177*x^101 + 26400664613*x^100 + 23851849790*x^99 + 21521499793*x^98 + 19393617918*x^97 + 17453125685*x^96 + 15685857870*x^95 + 14078488658*x^94 + 12618513241*x^93 + 11294238537*x# ^92 + 10094708495*x^91 + 9009686538*x^90 + 8029647723*x^89 + 7145704429*x^88 + 6349587741*x^87 + 5633643424*x^86 + 4990760988*x^85 + 4414352627*x^84 + 3898350489*x^83 + 3437146528*x^82 + 3025567470*x^81 + 2658870568*x^80 + 2332695429*x^79 + 2043040165*x^78 + 1786252409*x^77 + 1558990312*x^76 + 1358206138*x^75 + 1181130618*x^74 + 1025240398*x^73 + 888249964*x^72 + 768094894*x^71 + 662899405*x^70 + 570975786*x^69 + 490811551*x^68 + 421035657*x^67 + 360421915*x^66 + 307880930*x^65 + 262428980*x^64 + 223189856*x^63 + 189392667*x^62 + 160344810*x^61 + 135431808*x^60 + 114117746*x^59 + 95923935*x^58 + 80428483*x^57 + 67265736*x^56 + 56111173*x^55 + 46681006*x^54 + 38731301*x^53 + 32046021*x^52 + 26438475*x^51 + 21749899*x^50 + 17839141*x^49 + 14586067*x^48 + 11890042*x^47 + 9661071*x^46 + 7823149*x^45 + 6314467*x^44 + 5079078*x^43 + 4069867*x^42 + 3249925*x^41 + 2585598*x^40 + 2048369*x^39 + 1616541*x^38 + 1270768*x^37 + 994337*x^36 + 774662*x^35 + 600849*x^34 + 463822*x^33 + 356345*x^32 + 272173*x^31 + 206935*x^# 30 + 156685*x^29 + 117572*x^28 + 87739*x^27 + 65508*x^26 + 48207*x^25 + 35065*x^24 + 25832*x^23 + 18682*x^22 + 13080*x^21 + 9479*x^20 + 6821*x^19 + 4508*x^18 + 3162*x^17 + 2330*x^16 + 1434*x^15 + 920*x^14 + 730*x^13 + 427*x^12 + 217*x^11 + 201*x^10 + 122*x^9 + 36*x^8 + 43*x^7 + 34*x^6 + 3*x^5 + 5*x^4 + 8*x^3 + 1 # y := %; # 2000: 271 Electoral Votes # 2004: 286 Electoral Votes # 2008: 365 Electoral Votes # 2012: 332 Electoral Votes # 2016: 304 Electoral Votes # coeff(y, x, 271) = 16965465344318 # coeff(y, x, 286) = 16196017263096 # coeff(y, x, 365) = 3182416524832 # coeff(y, x, 332) = 8628577597686 # coeff(y, x, 304) = 13873406885786 # --------------------------------------- # Question 2 # Popularity Vote: # 2000: 48.4/(48.4+47.9) # 2004: 50.7/(50.7+48.3) # 2008: 52.9/(52.9+45.7) # 2012: 51.1/(51.1+47.2) # 2016: 46.1/(46.1+48.2) # 2000 Election: # evalf(coeff(GFvp(USEC(), 484/(484 + 479), x), x, 270)) = 0.007538873826 # evalf(add(seq(coeff(GFvp(USEC(), 484/(484 + 479), x), x, i), i = 270 .. 538))) = 0.5069967195 # 2004 Election: # evalf(coeff(GFvp(USEC(), 507/(507 + 483), x), x, 270)) = 0.007497274336 # evalf(add(seq(coeff(GFvp(USEC(), 507/(507 + 483), x), x, i), i = 270 .. 538))) = 0.5464029381 # 2008 Election: # evalf(coeff(GFvp(USEC(), 529/(529 + 457), x), x, 270)) = evalf(coeff(GFvp(USEC(), 529/(529 + 457), x), x, 270)) # evalf(add(seq(coeff(GFvp(USEC(), 529/(529 + 457), x), x, i), i = 270 .. 538))) = 0.6445533539 # 2012 Election: # evalf(coeff(GFvp(USEC(), 511/(511 + 472), x), x, 270)) = 0.007411975346 # evalf(add(seq(coeff(GFvp(USEC(), 511/(511 + 472), x), x, i), i = 270 .. 538))) = 0.5780307624 # 2016 Election: # evalf(coeff(GFvp(USEC(), 461/(461 + 482), x), x, 270)) = 0.007473511433 # evalf(add(seq(coeff(GFvp(USEC(), 461/(461 + 482), x), x, i), i = 270 .. 538))) = 0.4501744771 -------------------------------------------- # Question 3 # SimuCount(L, 3/10, N, K) = # [160.6440000, 46.98660728, 0.2650279441, 2.912817952], 0.4225000000 # evalf(StatAnal(GFvp(USEC(), 3/10, x), x, 4)) = # [161.4, 46.65683229710306854663607100641625378942, 0.2695069203525948108704969258325168219220, 2.844567676082227300797606389705762948010] # SimuCount(L, 2/5, N, K) = # [213.9915000, 49.68485109, 0.1192262487, 2.714988077], 0.2430000000 # evalf(StatAnal(GFvp(USEC(), 2/5, x), x, 4)) = # [215.2, 49.87825177369391321878676788607172528300, 0.1260503199154978322151205189258525816677, 2.769840597275605810796455615525841288400] # SimuCount(L, 1/2, N, K) = # [270.3190000, 51.51607749, -0.009752684694, 2.750812195], 0.1655000000 # evalf(StatAnal(GFvp(USEC(), 1/2, x), x, 4)) = # [269., 50.90677754484170843449304156677286845820, 0., 2.748917015209751793596133398755463223709] # SimuCount(L, 3/5, N, K) = # [322.8775000, 49.91534327, -0.2436110745, 3.070828346], 0.2355000000 # evalf(StatAnal(GFvp(USEC(), 3/5, x), x, 4)) = # [322.8, 49.87825177369391321878676788607172528300, -0.1260503199154978322151205189258525816677, 2.769840597275605810796455615525841288400] # SimuCount(L, 7/5, N, K); --> Error, (in StatAnal) numeric exception: division by zero # evalf(StatAnal(GFvp(USEC(), 7/5, x), x, 4)) = # Can't be made into a probability generating function # FAIL # SimuCount(L, 7/10, N, K) = # [376.7805000, 45.90495964, -0.2275565547, 2.882963927], 0.3950000000 # evalf(StatAnal(GFvp(USEC(), 7/10, x), x, 4)) = # [376.6, 46.65683229710306854663607100641625378942, -0.2695069203525948108704969258325168219220, 2.844567676082227300797606389705762948010] # The values from the simulations and the theoretical value in the four above runs are relatively close to one another, but # of course not exact.