4. 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. .

1. 4. 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.