Please help solve the following MATHEMATICAL STATISTICS problem:

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 p q (all three probabilities being between 0 and 1.) Let X be the rst time that red is chosen and Y the rst 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