If the random variables X and Y have joint probability density given by

(, ) = {

(1 +

3

), 0 < < 1, 0 < < 1

0,

.

Find marginal densities of X and Y. Find the conditional density of Y given X = 1

2

and

conditional density of X given Y= 1

4

. Find the correlation coefficient of X and Y. Find

linear regression of Y on X. Also, prove or disprove that X and Y are independent

random variables.