A fair 6-sided die is rolled, and then a coin with probability p of Heads is flipped as manytimes as the die roll says. (For example, if we roll a 3, then we flip the coin 3 times.) Let Xbe the result of the die roll and Y be the number of times the coin lands Heads.(a)  Find the joint PMF of X and Y . Write the answer as a table (b)  Find the marginal PMF of X.(c)  Find the marginal PMF of Y .(d)  Are X and Y independent? Why?(e)  Find the conditional PMF of X given Y = 2.

 A fair 6-sided die is rolled, and then a coin with probability p of Heads is flipped as many
times as the die roll says. (For example, if we roll a 3, then we flip the coin 3 times.) Let X
be the result of the die roll and Y be the number of times the coin lands Heads.
(a)  Find the joint PMF of X and Y . Write the answer as a table 
(b)  Find the marginal PMF of X.
(c)  Find the marginal PMF of Y .
(d)  Are X and Y independent? Why?
(e)  Find the conditional PMF of X given Y = 2.