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David and Peter independently choose at random a number from 1, 2, 3, with each possibility equally likely. Let X be the larger of the

David and Peter independently choose at random a number from 1, 2, 3, with each possibility equally likely. Let X be the larger of the two numbers, and let Y be the smaller.

a. Determine p(x, y).

b. Determine pX(x), x =1, 2, 3.

c. Determine pY|X(y|x).

d. Determine E(Y|X= x). Is this a linear function of x?

e. Determine V(Y|X = x)

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