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hw5_soln

# hw5_soln - Probability and Stochastic Processes A Friendly...

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Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers Roy D. Yates and David J. Goodman Problem Solutions : Yates and Goodman,3.1.2 3.1.4 3.2.3 3.2.5 3.3.3 3.3.5 3.4.1 and 3.4.6 Problem 3.1.2 On the X Y plane, the joint PMF is y x P X Y x y 3 c 2 c c c c c 2 c 3 c 1 2 1 (a) To find c , we sum the PMF over all possible values of X and Y . We choose c so the sum equals one. x y P X Y x y x 2 0 2 y 1 0 1 c x y 6 c 2 c 6 c 14 c Thus c 1 14. (b) P Y X P X Y 0 1 P X Y 2 1 P X Y 2 0 P X Y 2 1 c c 2 c 3 c 7 c 1 2 (c) P Y X P X Y 2 1 P X Y 2 0 P X Y 2 1 P X Y 0 1 3 c 2 c c c 7 c 1 2 (d) From the sketch of P X Y x y given above, P X Y 0. (e) P X 1 P X Y 2 1 P X Y 2 0 P X Y 2 1 P X Y 0 1 P X Y 0 1 8 c 8 14 1

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Problem 3.1.4 The sample space is the set S hh ht th tt and each sample point has probability 1 4. Each sam- ple outcome specifies the values of X and Y as given in the following table outcome X Y hh 0 1 ht 1 0 th 1 1 tt 2 0 The joint PMF can represented by the table P X Y x y y 0 y 1 x 0 0 1 4
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hw5_soln - Probability and Stochastic Processes A Friendly...

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