I am having trouble answering this question:
Suppose you have N quizzes that follow poisson distribution with parameter=K. The number of quizzes in which you pass is X and the probability that you pass in each is p. So X is binomially distributed with parameters N and p. What is the correlation between N and X?
I understand that we first find the covariance. Now, one problem I am having is that since these variables are dependent, I am not sure whether taking X|N would be a good place to start. With this approach, E(X) is np and E(N) is K. But how do we calculate E(NY)? the variances will also be found. Var(x)=np(1-p) and Var(N)=k. But is this approach right? How do we go about calculating E(XN) or should I use some other approach to calculate covariance and hence correlation?