You have two fair coins. The first coin is tossed five times. Let the random variable X be the number of heads showing up in these five tosses. The second coin is tossed X times. Let Y be the number...

You have two fair coins. The first coin is tossed five times. Let the random variable
X be the number of heads showing up in these five tosses. The second coin is tossed X
times. Let Y be the number of heads showing up in the tosses of the second coin.
What is the joint probability mass function of X and Y ? What is E(X + Y )?