HW8 - Chapter 5 Multivariate Probability Distributions 5.1...

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93 Chapter 5: Multivariate Probability Distributions 5.1 a. The sample space S gives the possible values for Y 1 and Y 2 : S AA AB AC BA BB BC CA CB CC ( y 1 , y 2 ) (2, 0) (1, 1) (1, 0) (1, 1) (0, 2) (1, 0) (1, 0) (0, 1) (0, 0) Since each sample point is equally likely with probably 1/9, the joint distribution for Y 1 and Y 2 is given by y 1 0 1 2 0 1/9 2/9 1/9 y 2 1 2/9 2/9 0 2 1/9 0 0 b. F (1, 0) = p (0, 0) + p (1, 0) = 1/9 + 2/9 = 3/9 = 1/3. 5.2 a. The sample space for the toss of three balanced coins w/ probabilities are below: Outcome HHH HHT HTH HTT THH THT TTH TTT ( y 1 , y 2 ) (3, 1) (3, 1) (2, 1) (1, 1) (2, 2) (1, 2) (1, 3) (0, –1) probability 1/8 1/8 1/8 1/8 1/8 1/8 1/8 1/8 y 1 0 1 2 3 –1 1/8 0 0 0 y 2 1 0 1/8 2/8 1/8 2 0 1/8 1/8 0 3 0 1/8 0 0 b. F (2, 1) = p (0, –1) + p (1, 1) + p (2, 1) = 1/2. 5.3 Note that using material from Chapter 3, the joint probability function is given by p ( y 1 , y 2 ) = P ( Y 1 = y 1 , Y 2 = y 2 ) = 3 9 3 2 3 4 2 1 2 1 y y y y , where 0 y 1 , 0 y 2 , and y 1 + y 2 3. In table format, this is y 1 0 1 2 3 0 0 3/84 6/84 1/84 y 2 1 4/84 24/84 12/84 0 2 12/84 18/84 0 0 3 4/84 0 0 0
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94 Chapter 5: Multivariate Probability Distributions Instructor’s Solutions Manual 5.4 a. All of the probabilities are at least 0 and sum to 1.
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This note was uploaded on 10/19/2011 for the course MATH MTH 540 taught by Professor Smith during the Fall '00 term at University of Alberta.

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HW8 - Chapter 5 Multivariate Probability Distributions 5.1...

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