Homework for MATH/STAT 511
Probability

Homework Assignments and Supplementary Materials

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No.	Assignment Due	Page and No.'s	Solutions
#1	Jan. 22 (Monday)	Page 73-74: (Sect. 2.1)   1,2,13
#2	Jan. 26 (Friday)	Page 82-85: (Sect. 2.2)   1, 3, 5, 8, 11
#3	Feb. 2 (Friday)	Page 82-85: (Sect. 2.2)  17, 18   Page 92-95: (Sect. 2.3)  1, 4, 7, 11, 17   EXTRA CREDIT ... P. 92-95:   15
#4	Feb. 9 (Friday)	Page 101-103: (Sect. 2.4)  3,5,9,11,12,16   Page 106: (Sect. 2.5)   1,5
#5	Feb. 14 (Wednesday)	Page 116-118: (Sect. 3.1)  3 a-c; 7; 11   Page 139: (Sect. 3.3)   3 a,b; 5 c,a
#6	Feb. 23 (Friday)	a)  Review the Excel spreadsheet (click here) for computing   distributions and plotting pmfs. Download the computer   experiments in the sheets 3-4 of the spreadsheet   PMF_2.xls (click here).   Note that there are 4 worksheets along the bottom tabs. b)   Page 139: (Sect. 3.3)   4 a),b),c); 11 c)   Use the spreadsheets in part a) to perform 100   experiments of randomly tossing a fair coin 5 times   and recording the number of heads. Plot the relative   frequencies and the computed probabilities.	Lecture #15 on Probabilistic Computer Simulations (Click Here ->).
#7	March 2 (Friday)	Page 127-128: (Sect. 3.2)  7; 14; 15 a-c; 21   Page 139-140: (Sect. 3.3)  5 d; 9; 13
#8	March 26 (Monday)	Page 151-152: (Sect. 3.4)  5; 7; 10; 11   For the negative binomial distribution, show that E[X2] = M''(0) = r(r+q)/p2   Page 161: (Sect. 3.5)  1; 3; 5; 9
#9	March 30 (Friday)	Problem 1: For the random variable with an exponential distribution, and mean waiting time parameter theta, show that E[X] is theta and the variance is theta^2.   Page 174: (Sect. 4.1)  1;8   Page 181-182: (Sect. 4.2)  3; 9a
#9 1/2	March 30 (Friday)	(Click Here ->) for the details of the derivation of the random variable which the Gamma distribution models.	.
#10	April 2 (Monday)	Page 191: (Sect. 4.3)  1; 9 a,c   Page 201: (Sect. 4.4)  1 a,b,c,d,f
#11	April 11 (Wednesday)	Web lecture: "Normal Random Variables    and the Chi-Squared distribution"
#12	April 20 (Friday)	Page 201-205: (Sect. 4.4)  5 a; 6; 21     Extra Credit: 20
#13	April 27 (Friday)	Page 233-235: (Sect. 5.1)  1 (all); 8 b,c,e   Page 242: (Sect. 5.2)  1; 10

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