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An experiment is repeated independently (at times 1, 2, 3,...) where in each experiment, one ball is chosen, red with probability p, green with

  

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 - p -q (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. (a) What are the marginal distributions of X and Y? (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. Hence write down the conditional probability mass function of X given Y = y. What is the conditional expectation of X given that Y = y? (c) (d)

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a The marginal PDFs for both x and y here would be geometric distribution as we are looki... blur-text-image

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