would anyone be able to help me with this question?
Consider a random variable $X$ with probability density function
$f(x) = xe^{−x^2/2}, x\geq 0.$
Determine x such that
$P(X \lt x) = 0.5$, $P(X \leq x) = 0.5$, and $P(X \gt x) = 0.95.$
What I've tried to do is integrate $f(x)$ to get $F(X)$ and then substitue in the different values of $F(X)$. However I haven't been getting real numbers as answers.