X and Z are two random variables. X is equal to 1 with probability 0.3, and equal to 0 with probability 0.7. You also know that E [Z | X = 1] = 10; and E [Z | X = 0] = 1: Compute E [Z]?
I am studying for an exam and am stuck on this review problem. I was thinking that
E[z] = E [Z | X = 1] + E [Z | X = 0]
but I think that is too simple. I would really appreciate some helpful hints. Thank you.