Question: 3. [Joint probability density functions] The jointly continuous random variables X and Y have joint pdf fX,Y (u, v) = 3 2 0 u <

3. [Joint probability density functions] The jointly continuous random variables X and Y have joint pdf fX,Y (u, v) = 3 2 0 u < 1, 0 v < 1, 0 u v < 1, 1 2 , 0 u < 1, 0 v < 1, 1 u v < 2, and zero elsewhere. (a) Determine the marginal pdf of X. (b) Determine the conditional pdf of Y given X. (c) Determine the marginal pdf of Y . (d) Determine the conditional pdf of X given Y . (e) Determine P{X Y 1/2}. (f) Determine P{X2 Y 2 1}

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