Question: 1. Let X be a Poisson random variable with a random parameter A, which has probability density function fA ( x ) = e-d, >

1. Let X be a Poisson random variable with a random parameter A, which has probability density function fA ( x ) = e-d, > > 0. Find the probability mass function of X. (Hint: The conditional probability mass funcion of X given A is fx A=x(x|A = A) = X"e- /x! for x = 0, 1, 2, ... and > > 0.)

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