#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

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

i. x^19 + x^19 + x^11 + x^17 + x^29 + x^18 + x^10
ii. 2x^65 + x^54 + x^66 + x^67 + x^62 + x^56

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 the first 10 presidents
ii. What is the weight enumerator of the set of the last 10 dead presidents according to age of death
iii. Consider the artificial set P1 * P2 with 100 elements and define F(Early President, Late President) = Sum of their ages when they died
Find the weight enumerator of the set P1*P2 according to F
iv. How many pairs have combined ages 120? 140? 160?

First 10 presidents:
[67, 83, 90, 73, 85, 68, 78, 80, 53, 65]
Weight enumerator:
x^67 + x^83 + x^90 + x^73 + x^85 + x^68 + x^78 + x^80 + x^53 + x^65

Last 10 presidents:
[63, 46, 90, 78, 88, 64, 81, 93, 93, 94]
Weight enumerator:
x^63 + x^46 + x^90 + x^78 + x^88 + x^64 + x^81 + 2x^93 + x^94

P1 * P2= 
[[130], [113], [157], [145], [155], [131], [148], [160], [160], [161], [146], [129], [173], [161], [171], [147], [164], [176], [176], [177], [153], [136], [180], [168], [178], [154], [171], [183], [183], [184], [136], [119], [163], [151], [161], [137], [154], [166], [166], [167], [148], [131], [175], [163], [173], [149], [166], [178], [178], [179], [131], [114], [158], [146], [156], [132], [149], [161], [161], [162], [141], [124], [168], [156], [166], [142], [159], [171], [171], [172], [143], [126], [170], [158], [168], [144], [161], [173], [173], [174], [116], [99], [143], [131], [141], [117], [134], [146], [146], [147], [128], [111], [155], [143], [153], [129], [146], [158], [158], [159]]
Weight enumerator of this would be x^130 + x^113 + x^157+...

0 pairs have combined ages 120, 0 pairs have combined ages 140, 2 pairs have combined ages 160

3.
Look up in the internet 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)
Then find m4^2/m2^2 (in other words, find the kurtosis)

Top 10 dead rock singers of all time:
1. Freddie Mercury (45)
2. Jimi Hendrix (27)
3. Kurt Cobain (27)
4. Bob Marley (36)
5. Buddy Holly (22)
6. John Lennon (40)
7. Prince (57)
8. Elvis Presley (42)
9. Jim Morrison (27)
10. David Bowie (69)

Mean: 39.2
Variance (m2): 4999/25
Kurtosis (m4): 65267647/625
m4^2/m2^2 : 4259865744916609/15618750625