Let X and Y be random variables With joint density function aw) = Cwaw - w)(1 - ml, 0 lt; 93 lt; y lt; 1, where (1,6,7 are all positive...

Let X and Y be random variables with joint density function.. (see the attached picture for complete question)

Let X and Y be random variables With joint density functionflaw) = Cwaw - w)fi(1 - ml, 0 < 93 < y < 1, where (1,6,7 are all positive parameters.(a) Find the normalizing constant C;(b) Determine the marginal distributions of X and Y;c) Show that the random variables % and Y are statistically independent;(d) Using the result in Part (c) , derive an expression for the covariance 002) (X , Y).