Can anyone help with the following question please?
The continuous random variables X and Y have the joint probability density function,
f XY (x,y) = 6x, 0 < x < 1, 0 < y < 1-x
Derive the marginal p.d.f for X and Y, and find the marginal expected values for both X and Y.
For the marginal of X, I got 3x(1-x) using the limits of 0 to 1-x
and for Y I got 3, using the limits of 0 to 1.
And using the limits from 0 to 1, I got E(X) = 1/4
My question is what limits, would I used for E(Y), as when I use 0 to 1-x I get E(Y) = (1-x)^3 - 3(1-x)^2