# Question: A fair six sided die is rolled 30 independent times Let

A fair six-sided die is rolled 30 independent times. Let X be the number of ones and Y the number of twos.

(a) What is the joint pmf of X and Y?

(b) Find the conditional pmf of X, given Y = y.

(c) Compute E(X2 − 4XY + 3Y2).

(a) What is the joint pmf of X and Y?

(b) Find the conditional pmf of X, given Y = y.

(c) Compute E(X2 − 4XY + 3Y2).

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