I'm just starting a new module of probability, and I get the sense that these are supposed to be revision questions, but I don't seem to be able to work it out. :S
If X and Y are uniformly distributed continuous random variables on (0,1), then how would I work out P(X^2 + Y^2 <= 1)?
I've looked through all my past probability work and lecture examples and I can't find anything similar. I know that P(X <= x) = x and P(Y <= y) = y, but how can you combine these, since they depend on each other?
Thanks for any and all help!