Thread: [SOLVED] Expectation of a Conditional Distribution

I am stuck in this problem

Let X and Y have the joint pdf zero elsewhere. Show that, on the set of positive probability density, the graph is a straight line whereas that of is not a straight line.

Here's what I have so far, I am not sure if it's right though

The marginal pdf of X is
for

So the conditional is
for

???

What are the limits of integration for the marginal pdf of Y??

0<x<1

E(Y|x)=\int^{x} _{-x} \frac{y}{2x}dy=\frac {y^2}{4x} |^{x} _{-x}=\frac{x^2-x^2}{4x}=0???

Correct

What are the limits of integration for the marginal pdf of Y??

f_2(y)=\int ^?_? f(x,y)dx

if you know that Y = y, then we have the restriction -x<y<x as well as 0<x<1.
, and together with x>y this gives x>|y|.
So the limits are |y|<x<1.