## Question

###### Suppose $X$ is a Poisson random variable with mean $lambda$. The parameter $lambda$ is itself a random variable whose distribution is exponential with mean 1. Show that $P[X=n]=left(frac{1}{2}ight)^{n+1}$.

Suppose $X$ is a Poisson random variable with mean $lambda$. The parameter $lambda$ is itself a random variable whose distribution is exponential with mean 1. Show that $P[X=n]=left(frac{1}{2} ight)^{n+1}$.

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