#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

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Attendance Question 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

S = {Kelvin: 29, Newton: 32, Veronica: 39, Stephanie: 35, Jessie: 40, Kenny: 29}

i) 2*x^29 + x^32 + x^35 + x^39 + x^40

ii) (using inches)
x^51 + 2*x^52 + x^53 + x^58 + x^59

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Attendance Question 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. 
ii)  What is the weight enumerator of the set of last 10 dead presidents.
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?

i) x^53 + x^65 + x^67 + x^68 + x^73 + x^78 + x^80 + x^83 + x^85 + x^90
ii) x^46 + x^63 + x^64 + x^78 + x^81 + x^88 + x^90 + 2*x^93 + x^94

iii) 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) No pairs have combined age 120 or 140. 2 pairs have combined age 160.


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Attendance Question 3:
Look up in the internet the Top 10 dead rock singers of all time
Find the average age at death, the variance (2nd moment about the mean) m2 and the fourth moment about the mean m4
Then find the m4/m2^2 (In other words find the kurtosis)

L := [45, 27, 27, 36, 22, 40, 57, 42, 27, 69]
Average age at death: 196/5 = 39.2
m2 = 4999/25 = 199.96
m4 = 65267647/625 = 104428.2352

kurtosis = 65267647/24990001 = 2.61175047572