Suppose Λ is an exponential random variable with mean 1. Conditional on Λ = λ, N is a…

Suppose Λ is an exponential random variable with mean 1. Conditional on Λ = λ, N is a Poisson random variable with parameter λ.

(a) Find E[N|Λ] and V [N|Λ]

(b) Use the law of total expectation to find E[N].

(c) Use the law of total variance to find V [N].

(d) Find the probability mass function of N.

(e) Find E[N] and V [N] again using the pmf of N.

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