Question

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Problems 133 5.3 Let X and Y have the following joint PMF 0.1 0.1 0.1 0.1 0 0.0 0.1 0.2 0.3 o-一ㄒㄧㄒㄧ丁 a. What are the marginal PMFs of X and Y? b. What are the conditional probabilities (computed directly) of X given Y and Y giw X (compute them directly)? c. What are the conditional probabilities of Y given X from the conditional probabilit of X given Y using Bayes theorem? Using the probabilities in Problem 5.3 a. What are E[X]. E[Y]. VarX], VarY], and Cov[x,Y] b. Are X and Y independent? Continue the example in Section 5.4, andconsider thejoint transformation, U=min (eg, min (3,2) = 2), and W = max (X, Y). For each transformation: a. What are the level curves (draw pictures)? b. What are the individual PMFs of U and W? c. What is the joint PMF of U and W? 5.4 5.5 5.6 Continue the example in Section 5.4, and consider the joint transformation V 2 and V - 2Y -X. For each transformation: a. What are the level curves (draw pictures)? b. What are the individual PMFs of V and V'? c. What is the joint PMF of V and V? 5.7 X and Y are jointly distributed as in the figure below. Each dot is equally likely a. What are the first-order PMFs of X and Y? b. What are Ex] and E[Y]? c. What is Cov[X, Y]? Are X and Y independent? d. If W = X-Y, what are the PMF of w and the mean and variance of w?

Answer 1

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