#ATTENDANCE QUIZ FOR LECTURE 12 of Dr. Z.'s Math454(02) Rutgers University

# Please Edit this .txt page with Answers

#Email  ShaloshBEkhad@gmail.com 
#Subject: p12
#with an attachment called
#p12FirstLast.txt
#(e.g. p12DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 13, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

PLEASE LIST ALL THE QUESTIONS FOLLOWED, AFTER EACH BY THE ANSWER

1) List the set of all your siblings and first cousins 
for each of them list their age. 
(i)Find the weight-enumerator according to age
(ii)According to height

I just did the ones that I can guess.
[18,19,17,26] -> x^26 + x^19 + x^18 + x^17
[160,157,172,155] -> x^172 + x^160 + x^157 + x^155

2) Look up in wikipedia the list of ages at death of dead presidents of USA

(i)What is the weight-enumerator of the set of first 10 dead presidents, P1
[67,83,90,73,85,68,78,80,53,65]->x^90 + x^85 + x^83 + x^80 + x^78 + x^73 + x^68 + x^67 + x^65 + x^53

(ii)What is the weight-enumerator of the set of last 10 dead presidents, P2
according to age at death
[94,93,93,81,64,88,78,90,46,63]->x^94 + 2*x^93 + x^90 + x^88 + x^81 + x^78 + x^64 + x^63 + x^46

(iii)Consider the artificial set P1xP2 with 100 elements and 
define the F(EarlyPresident, LatePresident)=Sum of their ages when they died
Find the weight-enumerator of the set P1xP2 according to F
WtEn(CP([67, 83, 90, 73, 85, 68, 78, 80, 53, 65], [94, 93, 93, 81, 64, 88, 78, 90, 46, 63]), x) ->
x^184 + 2*x^183 + x^180 + x^179 + 3*x^178 + x^177 + 2*x^176 + x^175 + x^174 + 4*x^173 + x^172 + 4*x^171 + x^170 + 3*x^168 + x^167 + 4*x^166 + x^164 + 2*x^163 + x^162 + 6*x^161 + 2*x^160 + 2*x^159 + 4*x^158 + x^157 + 2*x^156 + 2*x^155 + 2*x^154 + 2*x^153 + x^151 + 2*x^149 + 2*x^148 + 2*x^147 + 5*x^146 + x^145 + x^144 + 3*x^143 + x^142 + 2*x^141 + x^137 + 2*x^136 + x^134 + x^132 + 4*x^131 + x^130 + 2*x^129 + x^128 + x^126 + x^124 + x^119 + x^117 + x^116 + x^114 + x^113 + x^111 + x^99

(iv)How many such pairs have combined ages 120? 140? 160?
0,0,2

3) Look up in the internet the top ten dead rock singers of all time
Find their average age at death, the variance (2nd moment about the mean)
call it m2
and the fourth moment about the mean call it m4
Then find the ratio m4/m2^2 (in other words find the kurtosis)

[40,27,27,27,42,45,27,58,32,32]->
average = 35.7
variance: kthMomentClever([40, 27, 27, 27, 42, 45, 27, 58, 32, 32], 2)
m2 = 97.21
fourth moment about mean: kthMomentClever([40, 27, 27, 27, 42, 45, 27, 58, 32, 32], 4)
m4 = 27998.5777

m4/m2^2/kurtosis=2.96288014665