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

ANSWER:

Eli - 22yo, 71in, 
Ella - 29yo, 65 in, 
Eugene - 30yo, 63 in, 
Anna - 25yo, 60 in, 
Jennifer - 18yo, 63in

(i) f:=x^18 + x^22 + x^25 + x^29 + x^30
(ii) f:= x^60 + 2*x^63 + x^65 + x^71


QUESTION #2:

Look up the list of ages at death of presidents.
(i) What is the weight-enumerator of first 10 dead presidents of USA (P1)
(ii) What is the weight-enumerator of last 10 dead presidents (P2)
(iii) Consider the artificial set P1 x P2 with 100 elements and define F(EarlyPresident, LatePresident)=sum of their ages when they died. Find the weight-enumerator of set P1 x P2 according to F.
(iv) How many such pairs have combined ages 120? 140? 160?

ANSWER;

Ages of deaths of the first 10 presidents:
L1:=[67, 83, 90, 73, 85, 68, 78, 80, 53, 65]

Ages of deaths of the last 10 presidents:
L2:=[94, 93, 93, 81, 64, 88, 78, 90, 46, 63]

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

(iii) Running CP(L1,L2):
L:=[161, 160, 160, 148, 131, 155, 145, 157, 113, 130, 177, 176, 176, 164, 147, 171, 161, 173, 129, 146, 184, 183, 183, 171, 154, 178, 168, 180, 136, 153, 167, 166, 166, 154, 137, 161, 151, 163, 119, 136, 179, 178, 178, 166, 149, 173, 163, 175, 131, 148, 162, 161, 161, 149, 132, 156, 146, 158, 114, 131, 172, 171, 171, 159, 142, 166, 156, 168, 124, 141, 174, 173, 173, 161, 144, 168, 158, 170, 126, 143, 147, 146, 146, 134, 117, 141, 131, 143, 99, 116, 159, 158, 158, 146, 129, 153, 143, 155, 111, 128]

Running WtEn(L, x):
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)
Number of pairs with combined age 120: 0
Number of pairs with combined age 140: 0
Number of pairs with combined age 160: 2


QUESTION #3:

Look up the top ten 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. Find m4/m2^2 (kurtosis).

ANSWER:

List of ages of top 10 rock artists:
L:=[45,42,69,28,27,40,27,58,28,53]

Running Ave(L) gives:
41.7 years old at age of death.

The second moment, found by kthmoment(L,2):
m2 = 196.01

The fourth moment, found by kthMoment(L,4):
m4 = 80632.48970

The kurtosis:
m4/m2^2 = 2.098715705