I need help with these two 2nd year university statistics problem:

Q.1 Let the discrete random variable of Y have a conditional uniform probability distribution on {1,2,. x}; ie:
P(Y=y|X=x)=1/x, y=1,2,. x.
Determine the unconditional mean and variance of Y in terms of the mean and variance of the conditioning random variable X.

Q.2 Let the random variable Y have a conditional Poisson distribution, for x>0:
P(Y=y|X=x)=x^ye^(-x)/y!; y=0,1,2,. infinity
so that the conditional mean E(Y|X=x) and conditional variance Var (Y|X=x) are both equal to x. If X is equal to z1 with probability 1-p or z2 with probability p, determine the unconditional mean and variance of Y, and the actual probability distribution of Y.

Thanks,
Tania

How do you need help with the problems? What do you think the answers should be? And, how did you arrive at the answers? Please see the following link.

https://www.askmehelpdesk.com/math-s...board-b-u.html

I just don't know how to start these questions. How do I find the mean and variance?