Question

Let X and Y be continuous random variables with joint pdf fx y (x, y)-3x, 0 Sy and zero otherwise. 2. sx, a. What is the marginal pdf of X? b. What is the marginal pdf of Y? c. What is the expectation of X alone? d. What is the covariance of X and Y? e. What is the correlation of X and Y?

Answer 1

a) The marginal PDF of X is given by

b) The marginal PDF of Y is given by

c) The expected value is

d) Covariance is given by

$Cov(X,Y)=E(XY)-E(X)E(Y)~~~~~~~~~~~(1)$

Now

and

Hence, by (1) we get

Cor(X,Y) = 3 . 3 x 3 )10 4 4 10 4X4=-0.2625