Consider an urn containing four balls: a yellow ball with the number 1 on it, a

Question

Consider an urn containing four balls: a yellow ball with the number 1 on it, a red ball with the number 1 on it, a yellow ball with the number 2 on it, and a red ball with the number 2 on it. Suppose that two of these balls wil be randomly drawn from the urn. Letting X be the absolute value of the dierence of the numbers on the two balls (so X can only assume the values 0 (if the two balls have the same number on them) and 1 (if the two balls have dierent numbers on them)) and letting Y be the number of colors obtained (so Y can only assume the values 1 (if the two balls are the same color) and 2 (if the balls are dierent colors)), give the joint pmf of X and Y, using a tabular form similar to that used in Problem 1 on p. 342 of the text.

Explanation / Answer

ley y1 = yellow ball with number 1

y2 = yellow ball with number 2

r1 = red ball with number 1

r2 = red ball with number 2

sample space = { y1y2, y1r1, y1r2,y2r1,y2r2,r1r2}

P(0,1) = 0

P(0,2) = 1/6 + 1/6 = 1/3

P(1,1) = 1/6 + 1/6 = 1/3

P(1,2) = 1/3

joint PMF is

0

0

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