A fair die is rolled and then a coin with probabilty p of He

A fair die is rolled, and then a coin with probabilty p of Heads is flipped as many times as the die roll says,e.g. if the result of the die roll is a 3, then the coin is flipped 3 times. Let X be the result of the die roll and Y be the number of times the coin land Heads

a.) Find the joint PMF of X and Y. Are they independant

b.) find the marginal PMFs of X and Y

c.) Find the conditional PMFs of Y given X=x and of Y given X=x

Solution