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

  

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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 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) 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... View the full answer