1. Joint distribution

The joint distribution of X and Y is given by f(x,y)= (exp(-y)/y)
0<x<y<infinity
I need to compute E(X^2 + Y^2 | Y=y)

can anyone please guide me on how to do this.

Thank You very much for Your help

2. Using $\displaystyle f(x|y) = f(x,y) f(y),$ you can calculate the integral

$\displaystyle \iint \left(x^2 + y^2 \right) f(x|y)dxdy$

And to find $\displaystyle f(y)$ you have to calculate the integral

$\displaystyle \int_o^y f(x,y)dx$

3. Originally Posted by gustavodecastro
Using $\displaystyle f(x|y) = f(x,y) f(y),$

Why is this?

4. $\displaystyle E(X^2 + Y^2 | Y=y)= E(X^2|Y=y) + y^2$

and $\displaystyle E(X^2|Y=y)=\int x^2 f(x|y)dx$

5. is f(y) then =exp(-y) or Ei(-y)?
and if f(y) is equal to exp(-y)
is then
E(X^2+Y^2|Y0Y)
equal to [(exp(-2y)x^3)/3y]+[y^2] ?

really appreciate the help

6. Originally Posted by gustavodecastro
Using $\displaystyle f(x|y) = f(x,y) f(y),$ you can calculate the integral

$\displaystyle \iint \left(x^2 + y^2 \right) f(x|y)dxdy$

And to find $\displaystyle f(y)$ you have to calculate the integral

$\displaystyle \int_o^y f(x,y)dx$
is it dy or dx in the end of the integral defining f(y)?

7. dx

and

$\displaystyle f(x|y) = \frac{f(x,y)}{f(y)}$