How Do You Solve for Conditional Variance with a Given Joint Distribution?

[waealu]

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it.

If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution function of:

f(x,y) = 2x, for 0<x<1, x<y<x+1
otherwise 0.

How do I set up this question?

Thanks!

 

[Ray Vickson]

I am working on studying for a probability exam and I just came across conditional variance, but I can't find anything in my materials for how to solve it.

If I want to find the conditional variance of Y given that X=x, or Var[Y|X=x], how would I solve it? I am given a continuous distribution function of:

f(x,y) = 2x, for 0<x<1, x<y<x+1
otherwise 0.

How do I set up this question?

Thanks!

Set it up the standard way: first determine the conditional density f(y|X=x).

RGV