The document provides a joint probability density function (PDF) f(x,y)=C over the region 0≤y≤1, y≤x≤2 and asks to: 1) Find the marginal PDF fX(x) over its support and expected value E(X); 2) Find the marginal PDF fY(y) over its support and expected value E(Y).

1. 1. Suppose that ( X, Y ) is uniformly distributed over the region defined by
0 ? y ? 1, y ? x ? 2. That is, f( x, y ) = C, 0 ? y ? 1, y ? x ? 2, zero elsewhere
Find fX( x ). Be sure to include its support.
Find E( X ).
Find fY( y ). Be sure to include its support.
Find E( Y ).
2.Let X and Y be two random variables with joint p.d.f.
f( x, y ) = 64 x exp{
Solution
see problem number 15. this really helpful to you
http://www.stanford.edu/~henrya/math151/Hw6Sol.pdf