#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

#Q1:  List the set of all your sibilings and First Cousins. For each of them, list their Age. (23:31)
	(i) find the weight-Enumerator according to Age
	(ii) accordinig to height

	Brother: 22 height: 6'
	Cousin : 19 height: Unkown
	Cousin : 20 height: Unkown

	#Age= {22, 19, 20}
	 height={72}(inches)
	 A(i) f:= x^22+x^19+x^20
	 A(ii) g:= x^72
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#Q2: Look up in wikipedia the list of ages at death of dead presidents of USA(34:46)

		first and last10 presidents:
		1. 	George Washington 	67
		2. 	John Adams 		90
		3. 	Thomas Jefferson 	83
		4. 	James Madison 		85
		5. 	James Monroe 	 	73
		6. 	John Q. Adams 		80
		7. 	Andrew Jackson 	 	78
		8. 	Martin Van Buren  	79
		9. 	William Harrison 	68
		10. 	John Tyler 	 	71
		...	...			...
		31. 	Herbert Hoover 		90
		32. 	Franklin Roosevelt	63
		33. 	Harry Truman 		88
		34. 	Dwight Eisenhower	78
		35. 	John F. Kennedy 	46
		36. 	Lyndon Johnson 		64
		37. 	Richard Nixon 		81
		38. 	Gerald Ford 		93
		..	..			...
		40. 	Ronald Reagan 		93
		41. 	George Bush 		94


	(i) What is the weight-enumnerator of the set of first 10 dead presidents
	(ii) What is the weight-enumerator of the set of last 10 dead presidents

	# According to age at death

	(iii) Consider the artifical 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?


	#A:= 

	first={67.90,83,85,73,80,78,79,68,71}
	last={90,63,88,78,46,64,81,93,93,94}
	
	A(i)=x^67+x^90+x^83+x^85+x^73+x^80+x^78+x^79+x^68+x^71
	A(ii)=x^90+x^63+x^88+x^78+x^46+x^64+x^81+2x^93+x^94

	CP(first,last) = [113, 130, 131, 145, 148, 155, 157, 160, 161, 114, 131, 132, 146, 149, 156, 158, 161, 162, 117, 134, 135, 149, 152, 159, 161, 164, 165, 119, 136,
 	137, 151, 154, 161, 163, 166, 167, 124, 141, 142, 156, 159, 166, 168, 171, 172, 125, 142, 143, 157, 160, 167, 169, 172, 173, 126, 143, 144, 158, 161, 168, 170, 173,
 	174, 129, 146, 147, 161, 164, 171, 173, 176, 177, 131, 148, 149, 163, 166, 173, 175, 178, 179, 136, 153, 154, 168, 171, 178, 180, 183, 184]

	A(iii):x^184 + x^183 + x^180 + x^179 + 2*x^178 + x^177 + x^176 + x^175 + x^174 + 4*x^173 + 2*x^172 + 3*x^171 + x^170 + x^169 + 3*x^168 + 2*x^167 + 3*x^166 + x^165 + 	2*x^164 + 2*x^163 + x^162 + 6*x^161 + 2*x^160 + 2*x^159 + 2*x^158 + 2*x^157 + 2*x^156 + x^155 + 2*x^154 + x^153 + x^152 + x^151 + 3*x^149 + 2*x^148 + x^147 + 			2*x^146 + x^145 + x^144 + 2*x^143 + 2*x^142 + x^141 + x^137 + 2*x^136 + x^135 + x^134 + x^132 + 3*x^131 + x^130 + x^129 + x^126 + x^125 + x^124 + x^119 + x^117 + 
	x^114 + x^113

	A(iv): while there are no ages specifically in 120 and 140 (but 2 pairs in 160). There are 4 pairs in the 120s. 15 pairs in the 140s, 23 pairs in 160s.

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#Q3: 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) and the fourth moment about the mean (m2 and m4 respectivly) Find m4/m2^2 (find the kurtosis)(1:06:00)

	Top 10 dead rock stars
	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

	 Average: 39.2
	 Variance: 4999/25 (2nd moment about the mean)
	 fourth: 65267647/625 (4th moment about the mean)
	 Kurtosis:65267647/24990001