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## Homework Statement

Point is chosen at random (uniform PDF) within semi-circle: {(x,y)|x

^{2}+y

^{2}≤r

^{2}, y≥0}

Basically, I'm supposed to find E[X] for this problem

**2. The attempt at a solution**

I know how to do it, in a very long-winded fashion

(find f

_{Y}(y), and E[X|Y=y] etc).

But my teacher says that there is an easier way that doesn't involve a lot of calculations, anyone see it?

Thanks

EDIT;;;;

I think i might have gotten it, because the semicircle is an even function, the expected value of the first moment is 0. Can someone confirm this also?

Also, does this apply to a regular circle as well?

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