Thread: [SOLVED] Expected value of f(x,y) - Simple question

1. [SOLVED] Expected value of f(x,y) - Simple question

Ok, I know this is rather simple, but I need to refresh my memory on this:

f(x,y) = xy 0<x<y<1

I want to find E(x).

I know I should do E(x) = integral(1 to x), integral(0,y) [x*(xy)]dxdy.

However, I also know I've probably screwed up on the integration limits. Can somebody double check on this. My final answer should be a # right? Thanks

2. Originally Posted by spearfish
Ok, I know this is rather simple, but I need to refresh my memory on this:

f(x,y) = xy 0<x<y<1

I want to find E(x).

I know I should do E(x) = integral(1 to x), integral(0,y) [x*(xy)]dxdy.

However, I also know I've probably screwed up on the integration limits. Can somebody double check on this. My final answer should be a # right? Thanks
Note that $\displaystyle 0<x<y<1$. $\displaystyle x<y<1$ tells us that we are considering values above the line $\displaystyle y=x$ and below the line $\displaystyle y=1$. Also, we can conclude from restriction given that $\displaystyle x$ goes from 0 to 1.

Therefore, the integral should be $\displaystyle \int_0^1\int_x^1 x^2y\,dy\,dx$.

Does this make sense?

3. yeah, I can see what you're saying. I ll watch out for this next time.

4. I'd integrate the x first, that way both lower bounds of integration are zero.