Let $X$ be a random variable having continuous cumulative distribution function $F(x)$. What is the cumulative distribution function of $Y = \max(0, -X)$?
2026-03-31 18:26:17.1774981577
Cumulative distribution of $Y=\max(0,-X)$
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HINT
$$ F_Y(y) = \mathbb{P}[Y \le y] = \mathbb{P}[\max\{0,-X\} \le y] $$
When is $\max\{a,b\} \le y$? When both $a \le y$ and $b \le y$...