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Let N be a positive integer random variable with PMF of the form pN(n)=12⋅n⋅2−n,n=1,2,…. Once we...

Let N be a positive integer random variable with PMF of the form pN(n)=12⋅n⋅2−n,n=1,2,…. Once we see the numerical value of N , we then draw a random variable K whose (conditional) PMF is uniform on the set {1,2,…,2n} . 1. Find joint PMF pN,K(n,k) For n=1,2,… and k=1,2,…,2n 2. Find the marginal PMF pK(k) as a function of k . For simplicity, provide the answer only for the case when k is an even number. For k=2,4,6,… 3. Let A be the event that K is even. Find P(A|N=n) and P(A) .

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