#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 ----------------------------------------------------------------------------------------- 1. List the set of all your siblings and first cousins. For each of them list their ages. (i) Find the weight enumerator according to age L := [21, 26, 25, 33, 29, 13, 18, 20]; L := [21, 26, 25, 33, 29, 13, 18, 20] H := [160, 155, 171, 170, 166, 150, 160]; H := [160, 155, 171, 170, 166, 150, 160] WtEn(L, x); 33 29 26 25 21 20 18 13 x + x + x + x + x + x + x + x (ii) According to height H := [160, 155, 171, 170, 166, 150, 160]; H := [160, 155, 171, 170, 166, 150, 160] WtEn(H, x); 171 170 166 160 155 150 x + x + x + 2 x + x + x ----------------------------------------------------------------------------------------- 2. Look up on 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, P1 P1 := [67, 83, 90, 73, 85, 68, 78, 80, 53, 65]; P1 := [67, 83, 90, 73, 85, 68, 78, 80, 53, 65] WtEn(P1, x); 90 85 83 80 78 73 68 67 65 53 x + x + x + x + x + x + x + x + x + x (ii) What is the weight enumerator of the set of last 10 dead presidents, P2 P2 := [60, 63, 46, 90, 78, 88, 64, 81, 93, 93, 94]; P2 := [60, 63, 46, 90, 78, 88, 64, 81, 93, 93, 94] WtEn(P2, x); 94 93 90 88 81 78 64 63 60 46 x + 2 x + x + x + x + x + x + x + x + x (iii) Consider the artificial set P1 x P2 wth 100 elements and deffine the F := CP(P1, P2); F := [127, 130, 113, 157, 145, 155, 131, 148, 160, 160, 161, 143, 146, 129, 173, 161, 171, 147, 164, 176, 176, 177, 150, 153, 136, 180, 168, 178, 154, 171, 183, 183, 184, 133, 136, 119, 163, 151, 161, 137, 154, 166, 166, 167, 145, 148, 131, 175, 163, 173, 149, 166, 178, 178, 179, 128, 131, 114, 158, 146, 156, 132, 149, 161, 161, 162, 138, 141, 124, 168, 156, 166, 142, 159, 171, 171, 172, 140, 143, 126, 170, 158, 168, 144, 161, 173, 173, 174, 113, 116, 99, 143, 131, 141, 117, 134, 146, 146, 147, 125, 128, 111, 155, 143, 153, 129, 146, 158, 158, 159 ] WtEn(F, x); 184 183 180 179 178 177 176 175 x + 2 x + x + x + 3 x + x + 2 x + x 174 173 172 171 170 168 167 + x + 4 x + x + 4 x + x + 3 x + x 166 164 163 162 161 160 159 + 4 x + x + 2 x + x + 6 x + 2 x + 2 x 158 157 156 155 154 153 151 + 4 x + x + 2 x + 2 x + 2 x + 2 x + x 150 149 148 147 146 145 144 + x + 2 x + 2 x + 2 x + 5 x + 2 x + x 143 142 141 140 138 137 136 134 + 4 x + x + 2 x + x + x + x + 2 x + x 133 132 131 130 129 128 127 126 + x + x + 4 x + x + 2 x + 2 x + x + x 125 124 119 117 116 114 113 111 + x + x + x + x + x + x + 2 x + x 99 + x (iv) How many such pairs have combined ages 120? 140? 160? T := WtEn(F, x); 184 183 180 179 178 177 176 175 T := x + 2 x + x + x + 3 x + x + 2 x + x 174 173 172 171 170 168 167 + x + 4 x + x + 4 x + x + 3 x + x 166 164 163 162 161 160 159 + 4 x + x + 2 x + x + 6 x + 2 x + 2 x 158 157 156 155 154 153 151 + 4 x + x + 2 x + 2 x + 2 x + 2 x + x 150 149 148 147 146 145 144 + x + 2 x + 2 x + 2 x + 5 x + 2 x + x 143 142 141 140 138 137 136 134 + 4 x + x + 2 x + x + x + x + 2 x + x 133 132 131 130 129 128 127 126 + x + x + 4 x + x + 2 x + 2 x + x + x 125 124 119 117 116 114 113 111 + x + x + x + x + x + x + 2 x + x 99 + x coeff(T, x, 120); 0 coeff(T, x, 140); 1 coeff(T, x, 180); 1 ----------------------------------------------------------------------------------------- 3. Look up on the internet the top 10 dead rock singers of all time Find their average age at death, the variance (second moment about the mean) call it m2 and the fourth moment about the mean call it m4 Find m4/m2^2 (In other words find the KURTOSIS) A3. A := [40, 27, 27, 27, 42, 45, 27, 58, 32, 32]; A := [40, 27, 27, 27, 42, 45, 27, 58, 32, 32] Ave(A); 357 --- 10 m2 := kthMoment(A, 2); 9721 m2 := ---- 100 m4 := kthMoment(A, 4); 279985777 m4 := --------- 10000 m4/m2^2; 279985777 --------- 94497841 -----------------------------------------------------------------------------------------