Consider the following mixture distribution.

1. Draw \(X \sim \mbox{Ber}(p=.3)\)
2. If \(X=1\) then \(Y \sim \mbox{Geometric}(p_1)\)
3. If \(X= 0\) then  \(Y \sim \mbox{Bin}(n,p_2)\)

What is \(\mathbf{E}(Y)\) ?. (*) What is \(\mathbf{E}(Y | X )\) ?.