# Random variables with joint density function

Let R be the rectangle $\ \{(x, y); 0 <= x <= 2, 0 <= y<= 1\}$, and let $\ f(x, y) = >k(x^2+ y^2)$ on R and zero elsewhere.

(a) Find the value of k which makes f a joint density function.

(b) If X and Y are random variables with joint density function f(x, y), find

i. the marginal distributions of X and Y ;

ii. the expectations and variances of X and Y ;

iii. the covariance and correlation of X and Y .

For a) I set the double integral equal to 1 and got k = $\ 3\over10$

for b)I) I got: