A man selects a ball from an urn containing n balls numbered from 1 to n. The number he selects is the number of true coins he tosses to determine his prize. The variance of the number of heads he obtains is 55/16. If his prize is $1000 times the number of heads he obtains, determine his expected prize.
I'm having a hard time with this problem. I think you're supposed to use the double expectation theorems, i.e. Var(Y) = Var[E(Y|X)] + E[Var(Y|X)] and I think X~Unif[1,n] and Y~Bin(n=x,p=1/2) , but I'm not sure where to go from here. Thanks for any help!