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# 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 ...

## 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}\$. #### Similar Solved Questions

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