Mathematics

Mekhi Petersen

4 July, 13:19

A fair die is rolled, and then a coin with probability 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 lands

Heads.

(a) Find the joint PMF of X and Y. Are they independent?

(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.

+2

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