#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

# Question 1: List the set of all your siblings and first cousins for each of them list their age. Find the weight-enumerator
# according to age. According to height

# Answer 1: David, Shelley, Paige, Emma, Elliot S={23,27,29,13,19} 
# Weight Enumerator: x^13 + x^19 + x^23 + x^27 + x^29

# Question 2: Look up in Wikipedia the list of ages at death of presidents of USA?
# (i) What is the weight-enumerator of the set of first 10 dead presidents, P1
# (ii) What is the weight-enumerator of the set of last 10 dead presidents, P2
# According to age at death
# (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.Find the weight enumerator of the set P1xP2 according to F.
# (iv) How many pairs have combined ages 120? 140? 160?

# Answer 2:
# (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): 0 pairs sum to 120. 0 pairs sum to 140. 2 pairs sum to 160


# Question 3: Look up in the internet 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 (in other words find the kurtosis)

# John Lennon: 40 
# Jimi Hendrix: 27
# Kurt Cobain: 27
# Jim Morrison: 27
# Elvis Presley: 42
# Freddie Mercury: 45
# Janis Joplin: 27
# George Harrison: 58
# John Bonham: 32
# Keith Moon: 32

# Weight Enumerator: 4x^27 + 2x^32 + x^40 + x^42 + x^45 + x^58
# 2nd moment: 9721/100
# 4th moment: 279985777/10000
# m4/m2^2 = 279985777/94497841