Probability with two uniformly distributed random variables.

Question

Let us assume that $X\sim U(0, 1)$ and $Y\sim U(0, 1)$.

Calculate the following probability: $$ P(X^2\geq Y) $$

I have no idea how to start calculating this exression when I have two random variables in it.

Answer 1

Hint:

• Draw the square $[0,1]\times[0,1]$.
• Draw the curve $y=x^2$ in this square.
• Find the region where $y \leq x^2$.