Find the probability that $x^2 - 2ax + b$ has complex roots if the coefficients $a$ and $b$ are independent random variables with the common density
- uniform, that is $1/h$, and
- exponential, that is $\alpha e^{-\alpha x}$
This comes down to finding $P(a^2 \lt b)$. But since $a$ and $b$ are both random variables, would it be $P(a^2\lt b) = P(x\lt k)P(y \lt k^2)$? That doesn't seem particularly correct.