Question

A fair six-sided die is rolled 10 independent times. Let X be the number of ones...

A fair six-sided die is rolled 10 independent times. Let X be the number of ones and Y the number of twos.

(a) (3 pts) What is the joint pmf of X and Y?

(b) (3 pts) Find the conditional pmf of X, given Y = y.

(c) (3 pts) Given that X = 3, how is Y distributed conditionally?

(d) (3 pts) Determine E(Y |X = 3).

(e) (3 pts) Compute E(X2 − 4XY + Y2).

Math   Statistics-And-Probability   
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