E and Var of two variables

[Romi123]

From deck of 52 cards numbered by 1-13, (each number has 4 cards) we choose two cards without replacement, the sum of the cards is X.
Then, we toss a coin X times, Y is the number of times 'Heads' shown.
what is the expected value and variance of Y?

 

[Romsek]

Well you're going to have to come up with the probability distribution of Y. Can you do that?

 

[Steven G]

X=26, X=25,...X=3, X=2
Y=26, Y=25, ..., Y=2, Y=1, Y=0.
p(Y=26)=?, p(Y=25)=?, ... p(Y=0)=?