Problem 6 (20 points) Joint density function of two continuous random variable X and Y is given below f(x,y) = { 16y 0 x>2;0 < y < 1 otherwise a) (5 points) Show that the equation above is a joint density function b) (2 points) What is the probability of P(2 4; < y < ) c) (5 points) Find the marginal distribution functions of X and Y d) (3 points) Find out whether random variables X and Y are dependent or independent. e) (5 points) Calculate covariance and correlation coefficient between X and Y