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5. (15 points) A insect lays a large number of eggs. We know the number of eggs follows follows a Poisson distribution with parameter A. We also know that each eeg will survive with with probability 7r. If we let X be number of survivors and Y be number of eggs laid. 0 Find the joint probability mass function of X and Y. c Find the conditional expectation of X given Y = 3;, that is E(X |Y = y). c Find the marginal pmf of X and its expectation