Problem 2 An experiment is repeated independently (at times 1, 2, 3,...) where in each experiment, one ball is chosen, r

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Problem 2 An Experiment Is Repeated Independently At Times 1 2 3 Where In Each Experiment One Ball Is Chosen R 1 (70.3 KiB) Viewed 33 times

Problem 2 An experiment is repeated independently (at times 1, 2, 3,...) where in each experiment, one ball is chosen, red with probability p, green with probability q and blue with probability 1 - -(all three probabilities being between 0 and 1.) Let X be the first time that red is chosen and Y the first time that green is chosen. 1 pts (a) What are the marginal distributions of X and Y? 3 pts (b) Write down the joint probability mass function p(x, y) of X and Y. Be sure to specify the set of valid points (x, y). Hint: you should probably write the x > y and x < y cases separately. 2 pts (c) Hence write down the conditional probability mass function of X given Y = y. 2 pts (d) What is the conditional expectation of X given that Y = y?