Question: Poisson Random Variable with Exponentially Distributed Parameter Suppose that X follows a Poisson distribution with parameter , where is itself another random variable with distribution

Poisson Random Variable with Exponentially Distributed Parameter Suppose that X follows a Poisson distribution with parameter , where is itself another random variable with distribution Exponential(), > 0. a. ShowthatE(k)= k! forkN. k b. What is the distribution of X? c. Determine the conditional density of given X

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