#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. 16, 2020, 8:00pm


THE NUMBER OF ATTENDANCE QUESTIONS WERE:

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

Q1. 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 (better be integer) 

A1. 
    I only have 2 sibling. 
    Cousin A[age: 19, height: 175cm]
    Cousin B[age: 24, height: 184cm]

    (i). 
    Weight-Enumerator would be: f = x^19 + x^24
    (ii). 
    Weight-Enumerator would be: f = x^175 + x^184


Q2. Look up in Wikipedia the list of ages at death of dead presidents 
    (i). What is the weight enumerator of the set of first 10 dead presidents of USA -> 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 P1 X P2 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?

A2. 
    (i). 
        [P1]. f = x^67 + x^83 + x^90 + x^73 + x^85 + x^68 + x^78 + x^80 + x^53 + x^65
    (ii).
        [P2]. f = x^94 + x^93 + x^93 + x^81 + x^64 + x^88 + x^78 + x^90 + x^46 + x^63
    (iii). 
        P1 * 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). 
        120: 0
        140: 0
        160: 2


Q3. 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) [m2] 
    and the fourth moment about the mean [m4]. 
    Then find the ratio m4/m2^2 (in other words find the kurtosis)
A3. 
    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: x^40 + 4 * x^27 + x^42 + x^45 + x^58 + 2*x^32

    Average = subs(x = 1, diff(f, x))/subs(x = 1, f) = 35.7

    2nd moment = evalf(kthMomentClever(d, 2)) = 97.21
    4th moment = evalf(kthMomentClever(d, 4)) = 27998.57770