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| HomeworkSuggested study problems on the LLN and CLTConsider doing the following problems from the textbook: Grinstead-Snell, p312: 6, 7, 9 Homework 12, due Dec 10 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p280: 6, 18 And the following additional problem: A. Show that if X and Y are Poisson random variables, with parameters a and b, respectively, then X + Y is Poisson with parameter a + b. Homework 11, due Dec 1 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p250: 17, 22, 30ac And the following additional problem: A. Show that if X is a continuous random variable with Riemann density function f, then E( cX ) = cE( X ). Note: Depending on what version of the book you have, p263 30 may be p263 29. It is to calculate the variance of a Poisson random variable. Homework 10, due Nov 17 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p221: 23, 27, 37 Homework 9, due Nov 10 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p198: 8, 34 Homework 8, due Nov 3 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p159: 50 Homework 7, due Oct 27 at 2:07pmPlease do the following problems from the textbook:Grinstead-Snell, p150: 12, 15, 22, 26, 32, 39, 46, 54 Note: a bridge hand (as in problem 15) has 13 cards. Homework 6, due Oct 20 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p131: 1 And the following additional problem: A. Let m(w) be a uniform discrete probability distribution, and E be an event with P(E) > 0. Show that m( w | E ) is a uniform discrete probability distribution. Graded were p131: 1, and p160: 4, 8, 17. Homework 5, due Oct 13 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p115: 18, 29, 34a, 36 Note: you'll have to work hard for #36! Graded were p115: 29, 34a, 36a, and 4. Homework 4, due Oct 8 at 2:07pmPlease do the following problems from the textbook:Grinstead-Snell, p115: 6, 7, 10, 26 All problems were graded. Homework 3, due Sep 29 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p71: 6 And the following additional problem: A. Prove the identity in Problem 35 on p118 by examining the coefficient of x^{n} in ( 1 + x )^{2n}. Graded were p88: 11, 16; p115: 20; and Problem A. Homework 2, due Sep 22 at 2:07pmPlease do the following problems from the textbook:Grinstead-Snell, p71: 2, 3, 4, 8, 12, 14, 15, 16 Graded were p71: 2, 4, 12, 15. Homework 1, due Sep 15 at 2:07pmPlease do the following problems from the textbook: Grinstead-Snell, p13: 5 And the following additional problem: A. The code snippet linked here simulates n iterations of some random game, and counts the number of 'wins'. Describe the game played in terms of dice, coin flips, or some other appropriate 'real-world' terms. Note: In #17, log n is of course the natural log of n (base e, not base 10). Graded were p35: 6, 17, 31; Problem A. |