Question: 14. Each time you flip a certain coin, heads appears with probability p. Suppose that you flip the coin a random number N of times,

14. Each time you flip a certain coin, heads appears with probability p. Suppose that you flip the coin a random number N of times, where N has the Poisson distribution with parameter λ and is independent of the outcomes of the flips. Find the distributions of the numbers X and Y of resulting heads and tails, respectively, and show that X and Y are independent.

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