Question 5.

The joint density of two random variables X and Y is given by

f (x, y) = (x^2)y

whenever 0 < x < 1 and 0 < y < 4, and f (x, y) = 0 otherwise.

Are X and Y independent? Justify

your answer. Compute **E**X, and find the probability that X +Y is less than 3.

Well the problem is, you think that this is surely independent since it factors, but my teacher said something about how to be sure, you need to find the marginal densities and they need to multiply to give f(x,y), but when I compute the marginal densities, they don't which would mean they are dependent, but I could be doing something wrong, so any ideas which it is?

I can get EX, but for P(X+Y<3), can someone help set up the integral for me. I can compute it myself, but setting it up is the trouble.