A fair coin is flipped twice. Let X be the number of heads in the two tosses, and Y be the indicator r. v. for the tosses landing the same way. That is, Y is equal to 1 if the tosses land in the same way, and 0 otherwise. (a) Find the joint pmf of X and Y.

Step-by-step explanation:

It can be clearly observed that  and

Now lets find the probabilities of all possible combinations

Since it is impossible that the coin ha flipped in different ways given that all the time the tail has fallen

=1/2

=1/2

and similarly,