1. ## CDF?

I'm not even sure what this problem is asking. If someone could maybe re-phrase it, that might help clarify.

Problem:

Let X be a random variable having cumulative distribution function F(x). What is the cdf Y = max(0,-X)?

What does max(0,-X) mean?

Thanks!

2. Originally Posted by NoFace
I'm not even sure what this problem is asking. If someone could maybe re-phrase it, that might help clarify.

Problem:

Let X be a random variable having cumulative distribution function F(x). What is the cdf of Y = max(0,-X)?

What does max(0,-X) mean?

Thanks!
$\displaystyle \max(0,-X)$ is just the maximum of 0 and $\displaystyle -X$. In other words, if $\displaystyle X<0$ then $\displaystyle Y=-X$, and if $\displaystyle X\geq 0$ then $\displaystyle Y=0$. Notice that $\displaystyle Y\geq 0$ in any case.

Hence,
- if $\displaystyle t<0$, $\displaystyle P(Y\leq t)=0$;
- $\displaystyle P(Y\leq 0)=P(Y=0)=\cdots$;
- if $\displaystyle t> 0$, $\displaystyle P(Y\leq t)=P(Y=0)+P(0<Y\leq t)=\cdots$