#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



#ATTENDANCE Q. #1 for LECTURE 12
#List the set of all your siblings and first cousins
#for each of them list their age. Find the weight enumerator according to age and according to height

#ANSWER to Q. #1:	

# I don't have any siblings nor first cousins that I know of/met.  So, I will just make some ages/heights up:

# S = {A, B, C, D, E, F, G, H}
# age(A) = 12, age(B) = 10, age(C) = 22, age(D) = 6, age(E) = 3, age(F) = 15, age(G) = 24, age(H) = 10
# height(A) = 150, height(B) = 146, height(C) = 180, height(D) = 112, height(E) = 94, height(F) = 168, height(G) = 180, height(H) = 130 (cm)

# (i) f:= x^24 + x^22 + x^15 + x^12 + 2*x^10 + x^6 + x^3
# (ii) g:= 2*x^180 + x^168 + x^150 + x^146 + x^130 + x^112 + x^94




#ATTENDANCE Q. #2 for LECTURE 12
#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
#(ii) what is the weight-enumerator of the set of the last 10 dead presidents
#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 of the set P1xP2 according to F
#(iv) How many such pairs have combined ages 120? 140? 160?

#ANSWER to Q. #2:

#(i) f:= x^90+x^85+x^83+x^80+x^78+x^73+x^68+x^67+x^65+x^53
#(ii) g:= x^94+2*x^93+x^90+x^88+x^81+x^78+x^64+x^63+x^46
#(iii) h:= 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 for 120, 0 for 140, and 2 for 160




#ATTENDANCE Q. #3 for LECTURE 12
#Look up in the internet the top ten dead rock singers of all time
#find their average age at death, the variance m2, and the fourth moment
#about the mean m4, and find the ratio (m4/(m2)^2) (Kurtosis)

#ANSWER to Q. #3:

#using OLD RollingStone article from 2011, L:=[40,27,27,27,42,45,27,58,32,32]

#average age at death = Ave(L) = 357/10
# m2 = kthMomentClever(L,2) = 9721/100
# m4 = kthMomentClever(L,4) = 279985777/10000
# Kurtosis = 279985777/12744900