Questions on conditional and unconditional means and variances

I have a couple of questions in which I require to find the unconditional means and unconditional variances given the conditional probabilty distribution.

1. Suppose the random variable Y is given by P(Y=y|X=x)=(1-x)x^y. y=0,1,2,..,infinity; 0<x<1

I need to show that conditionally Var(Y|X=x)= E(Y|X=x)[1+E(Y|X=x)] and unconditionally Var(Y)=E(Y)[1+E(Y)]+2*Var(X/(1-X))

2. Let Y have the conditional binomial distribution P(Y=y|X=x)=(xCy)p^y(1-p)^(x-y); y=0,1,...,x; 0<p<1

If X has the Poisson distribution P(X=x)=w^x * exp(-w) / x!; x=0,1,..,infinity

once again I need to find the unconditional mean and variance of Y and the unconditional distribution of Y.

I more or less just need to know where to start. Any help will be greatly appreciated. Thanks in advance.