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Suppose that the number of eggs that a hen lays follows the Poisson distribution with parameter...

Suppose that the number of eggs that a hen lays follows the Poisson distribution with parameter λ = 2. Assume further that each of the eggs hatches with probability p = 0.8, and different eggs hatch independently. Let X denote the total number of survivors. (i) What is the distribution of X? (ii) What is the probability that there is an even number of survivors? 1 (iii) Compute the probability mass function of the random variable sin(πX/2) and its expectation.

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