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If the joint probability Distribution function of X and Y is F ( x , y ) = ( 1 e x ) ( 1 e y ) ; x 0 , y 0
(i) Obtain the joint density function of X, Y. (ii) Determine the marginal densities of X and Y .
(iii) Obtain the conditional densities of X and Y (iv) Are X and Y independent? (v) Is it true that
the conditional density function for an independent random variable same as that of its marginal
density? Justify with verbal reasoning.

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  • 1. If the joint probability Distribution function of X and Y is F ( x , y ) = ( 1 e x ) ( 1 e y ) ; x 0 , y 0 (i) Obtain the joint density function of X, Y. (ii) Determine the marginal densities of X and Y . (iii) Obtain the conditional densities of X and Y (iv) Are X and Y independent? (v) Is it true that the conditional density function for an independent random variable same as that of its marginal density? Justify with verbal reasoning.