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Unformatted text preview: f X  Y ( x ) . (c) [ 15 points ] Find the covariance of X and Y . Hint : The formulas or numeric values for all complicated integrals have been given to you. 3. [ 25 points ] The random variables X and Y have a joint probability density function of f XY ( x , y ) = b 2 ex2 y x 0 and y otherwise Find the joint probability density function of the random variables W and Z , where W = 2 XY Z = X2 Y Helpful formulas For a couple of problems, the following integral will be useful. i b a xeqx dx = eaq ( aq + 1 )ebq ( bq + 1 ) q 2 Also, useful information is that a random variable, e.g., Z , with probability density function f Z ( z ) = e z has E { Z } = 1 and E { Z 2 } = 2 2 . 2...
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 Spring '12
 MUNK

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