# Math Help - probability: conditioning and densities

1. ## probability: conditioning and densities

Suppose X, Y are random variables with joint density

f(x,y) = A^(3)xe^(-Ay) for 0<x<y
= 0 otherwise

a) What is the density of Y? What is E(Y)?
b) What is E(X|Y=1)?

--

2. Originally Posted by hanahou
Suppose X, Y are random variables with joint density

f(x,y) = A^(3)xe^(-Ay) for 0<x<y
= 0 otherwise

a) What is the density of Y? What is E(Y)?
b) What is E(X|Y=1)?

--
Marginal density: $f(y) = \int_0^y A^3xe^{-Ay}dx$
Expectation of Y: $E[Y] = \int_0^{\propto} y*f(y)dy$
For the second part, you need to find $f(x|y=1)$.