If X and Y are independent uniformly distributed random variables between 0 and 1, what is the probability that X^2+Y^2 is less than or equal to one.
P(Z<1) = P(X^2+Y^2<1)
For z between 0 and 1, P(X^2<z) = P(X < √z) = √z
The Attempt at a Solution
I'm a tad lost- I assume what you'd be looking for is the probability that Y^2 is less than or equal 1-X^2, or rather that Y is less or equal to √(1-X^2). Is that all there is to it?