Suppose X is a Poisson random variable with mean A. The parameter A is itself a random variable…

Suppose X is a Poisson random variable with mean A. The parameter A is itself a random variable whose distribution is exponential with mean Show that P(X = n] = (*)”+I. A coin is randomly selected from a group of ten coins, the nth coin having a probability n/10 of coming up heads. The coin is then repeatedly flipped until a head appears. Let N denote the number of flips necessary. What is the probability distribution of N? Is N a geometric random variable? When would N be a geometric random variable; that is, what would have to be done differently?

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