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Unformatted text preview: 2 if c-1 < x < c c if c < x < 2 c 1 / 4 if 2 c < x < 2 c + 1 (and equals zero for other values of x ), where c is a positive constant. ( a ) Find c and plot the density. ( b ) Compute and plot the cumulative distribution function of X . ( c ) Find P (0 < X ≤ 3 / 4 or X > 3 / 2), P ( X = 1) and P (the distance from X to the origin is greater than 1). Problem 3 A continuous random vector ( X,Y ) has a joint pdf given by f X,Y ( x,y ) = ± e-y if x-1 < y < x + 1 , y > otherwise . ( a ) Find the marginal probability densities of X and Y . Are X and Y independent? ( b ) Compute the probability P ( X + Y < 1). 1 Problem 4 Let Y 1 and Y 2 be independent standard uniform random variables. That is, each one of them has the density f ( y ) = 1 if 0 < y < 1, and 0 otherwise. Compute E h± max( Y 1 , 2 Y 2 )-min( Y 1 ,Y 2 ) ² 2 i . 2...
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This note was uploaded on 10/29/2011 for the course MATH 3310 at Cornell.