Uniform distribution find E(Y|x)

[confused88]

This is the question:

If X and Y have a uniform distribution over the circle x^2 + y^2 $$\leq$$ 9 find E(Y|x).

Can someone please explain to me, how to answer this question. You guys don't have to give me a solution, but a hint would be nice because I have no idea where to start. Thank you

 

[confused88]

well what i was thinking was that the range is between 3 and 0 and -3 and 0.

Then you integrate x^2 + y^2 with the first range (3 and 0) and then with -3 and 0. Is this right?

Or is the first range y to 3, and then -3 to 0?

I have no idea, please help me

 

[HallsofIvy]

"E(y|x)" means the mean value of y for a single value of x. There will only be an integral with respect to y, not x. x is fixed. y ranges between $-\sqrt{9- x^2}$ and $\sqrt{9- x^2}$. Your final answer for E(y|x) will be a function of x.

 

[confused88]

Thank you for replying. Yupp I think that i got the answer. I got zero at the end, but I'm pretty sure that's right