#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 the age 
(i) Find the weight enumerator according to age
(ii) according to height


Answer 1:

S= {Sanika, Abhijeet1, Abhijeet2, Mrinmayee, Pranjali, Shweta, Pratiek}
[20, 32, 29, 25, 29, 26, 26] - age in years
[66, 71, 66, 64, 63, 62, 66]- height in inches

(i) f(x)= Sum(x^(age(name)), name in S)


f(x)= x^20 + x^32 + 2*x^29 + x^25 + 2*x^26


(ii) g(x)= Sum(x^(height(name)), name in S)

g(x)= 3*x^66 + x^71 + x^64 + x^63 + x^62



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 P1 X P2 and define the combined weight 
F(early pres, late pres)= sum of ages when they died. Find weight enumerator of P1 X P2 according to F.
(iv) How many have combined ages 140? 120? 160?


Answer 2:


(i) P1= {67,83,90,73,85,68,78,80,53,65}

f(x)= x^67 + x^83 + x^90 + x^73 + x^85 + x^68 + x^78 + x^80 + x^53 + x^65


(ii) P2= {94,93,93,81,64,88,78,90,46,63}

g(x)= x^94 + 2*x^93 + x^81 + x^64 + x^88 + x^78 + x^90 + x^46 + x^63 


(iii) 

F(early_pres, late_pres)= f(x) + g(x)

|P1 X P2|_x = x^F(67,94) + x^F(67,93) + ... + x^F(67,63) +
              x^F(83,94) + x^F(83,93) + ... + x^F(83,63) +
	      .
	      .
	      .
	      x^F(65,94) + x^F(65,93) + ... + x^F(65,63)


(iv)
120 - none
140 - none
160 - none





Question 3:

Look up in the internet the top 10 dead rock singers of all time. 
(i) Find the average age at death
(ii) Variance (second moment about mean) and fourth moment about mean
(iii) Kurtosis - m4/(m2^2)

Answer 3:
Source: https://www.ranker.com/crowdranked-list/rock-stars-whose-deaths-were-the-most-untimely

A= {45, 27, 27, 36, 22, 40, 58, 42, 27, 69}

(i) 

L:=[45, 27, 27, 36, 22, 40, 58, 42, 27, 69]
L := [45, 27, 27, 36, 22, 40, 58, 42, 27, 69]
WtEn(L,x)
x^69+x^58+x^45+x^42+x^40+x^36+3*x^27+x^22
AveClever(L)
393/10

(ii)

kthMomentClever(L,2)
m2:=20361/100


kthMomentClever(L,4)
m4:=1059833937/10000

(iii)

Kurtosis

kthMomentClever(L,2)/(kthMomentClever(L,2)^2)
100/20361