Question

For all problems on this page, use the following setup:

Let N be a positive integer random variable with PMF of the form

pN(n)=1/2⋅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}.

Write down an expression for the joint PMF pN,K(n,k).

For n=1,2,… and k=1,2,…,2n:

pN,K(n,k)=

Answer 1

TOPIC:Joint pmf from the conditional pmf and the marginal pmf.