#ATTENDANCE QUIZ FOR LECTURE 8 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
#p8FirstLast.txt
#(e.g. p8DoronZeilberger.txt)

#Right after finishing watching the lecture but no later than Oct. 1, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE: 3

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

Question 1: List the set of all your siblings and First cousins
for each of them list them. 
Find the weight enumerator accoridng to age
ii) according to height
Name - age height
Vrinda - 15 5.5
Ariya - 12 5
Aarushi 25 5.8
Neil - 18 6.3
Avyaan - 5 4

Wt-enumerator(age) = x^15+x^12+x^25+x^18+x^5
Wt-enumerator(height) = x^5.5+x^5+x^5.8+x^6.3+x^4


Question 2: Look up in wikipedia the list of ages of death of death presidents of USA
(i) What is the weight enumerator of the set of First 10 presidents
p1 := 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 last 10 presidents
p2 := x^94 + 2*x^93 + x^90 + x^88 + x^81 + x^78 + x^64 + x^63 + x^46
(iii) Consider the artifical set p1*p2 with 100 elements
F := 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
define the F(EarlyPresident, LatePresident) = Sum(of their ages when they died)
Find the weight enumertor of the set according to F
(iv) How many such pairs have combined ages 120?140?160?
120 - 0
140 - 0
160 - 2

Question 3: the Top ten dead rock singers of all time
Find the average age at death, the variance, and the fourth moment about the mean call it m4
Then find the ratio m4/m2^2 

        p34 := [69, 58, 45, 42, 40, 36, 27, 27, 27, 22]
Ave(p34)
                              393
                              ---
                              10 
kthMoment(p34, 2)
                             20361
                             -----
                              100 

kthMoment(p34, 2)
                             20361
                             -----
                              100 
kthMoment(p34, 4)
                           1059833937
                           ----------
                             10000   
%/%%
                           353277979
                           ---------
                            678700