Let X and Y have a uniform distribution on the set of points with integer coordinates in

Chapter 4, Problem 4.3-9

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QUESTION:

Let X and Y have a uniform distribution on the set of points with integer coordinates in S = {(x, y): 0 x 7, x y x + 2}. That is, f(x, y) = 1/24, (x, y) S, and both x and y are integers. Find (a) fX (x). (b) h(y | x). (c) E(Y | x). (d) 2 Y | x. (e) fY (y).

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QUESTION:

Let X and Y have a uniform distribution on the set of points with integer coordinates in S = {(x, y): 0 x 7, x y x + 2}. That is, f(x, y) = 1/24, (x, y) S, and both x and y are integers. Find (a) fX (x). (b) h(y | x). (c) E(Y | x). (d) 2 Y | x. (e) fY (y).

ANSWER:

Step 1 of 7

(a) Note that 3 values of Y correspond to each value of X. The marginal p.m.f. of X is

         

 

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