#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: 3


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 ages. (i) find the weight-enumerator according to age and (ii) according to height 
A: 


(i) According to age
#Rayan, Zarmina, Sabrina, Farris C = {R, Z, S, F}
#age(R) = 18, age(Z) = 20, age(S) = 26, age(F) = 23
f := x^18 + x^20 + x^26 + x^23 


(ii) According to height
#Rayan, Zarmina,Sabrina, Farris C = {R, Z, S, F}
#height(R) = 72, height(Z) = 63, height(S) = 63, height (F) = 71
F := x^72 + x^63 + x^63 + x^71


2. (i) What is the weight enumerator of the set of the first 10 dead presidents, P1?
(ii) Last 10 dead presidents, P2?
(iii) Consider P1 X P2 with 100 elements and define F(EarlyPresident, LatePresident) = Sum of ages when they died. Find the weight enumerator of the set P1 X P2 according to F. 
(iv) How many such pairs have combined ages 120? 140? 160? 


A:


(i) P1 = x^67 + x^83 + x^90 + x^73 + x^85 + x^68 + x^78 + x^80 + x^53 + x^65
(ii) P2 = x^63 + x^46 + x^90 + x^78 + x^88 + x^64 + x^81 + 2*x^93 + x^94
(iii) P1 x P2 = 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) 120 - 0 pairs, 140 - 0 pairs, 160 - 2 pairs 


3. Who are the top 10 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 m4/m2^2 (kurtosis).


A: 


Top10 := [40, 27, 27, 27, 42, 45, 27, 58, 32, 32] 
Average age at death: 35.7
Variance/m2: 9721/100
M4: 279985777/10000
Kurtosis: 279985777/94497841