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Unformatted text preview: 1 and x < y < 1 and such that if ( X,Y ) has joint density f ( x,y ) then X is uniform (0 , 1). (b) Show there is no probability density function g ( x,y ) such that g ( x,y ) = 0 unless 0 < x < 1 and x < y < 1 and such that if ( Z,W ) have joint density g ( x,y ) then both Z and W are uniform on (0 , 1). (25) 5. Three balls are drawn at random with replacement from an urn containing 10,000 balls numbered from 1 to 10,000. (a) Find the probability that the median of the three numbers on the balls is 5000. (The median is the middle number: 5,3,4 has median 4 as does 5,4,4). (b) Is the probability that the average of the three numbers drawn equals 5000 larger, smaller, or the same as the answer to (a)? Prove your answer....
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- Spring '09