Math Help - Transformation of the exponential distribution

1. Transformation of the exponential distribution

At least I think that's the sort of thing the question's aiming at...

John and Jane have arranged to meet at a given time, and each, independently, will be late by an amount of that time that is exponentially distributed with parameter $\lambda$. Let $X$ and $Y$ denote the amount of time that John and Jane are late respectively.

Suppose that we are interested in the length of time that Jane arrives before John, that is, in $W=X-Y$. For $w\geq0$, show that

$F_W(w)=P(X-Y\leq w)=1-\frac{1}{2}e^{-\lambda w}$

Seriously do feel like this isn't all that complicated, but I just keep hitting a wall.

I attached the past paper this question comes from - it's question B6, part (b), part (ii).

2. I have literally no idea how to sketch that

3. Wow, you're a jerk. I love how you asked that question, then presumed you knew the answer...

I thought you meant sketch the $1-\frac{1}{2}e^{-\lambda w}$ thing.

So how's about, instead of getting insulting, you just walk me through it huh? I just want someone to show me how to do it in full; that's how I learn. Not by being suggested things then being patronised when I don't get it.

I don't know where you're getting the 2 from, either, so maybe you could explain that?

4. Yeah, you are the jerk. I haven't tried to help anyone on this site 'cause I can't, all of my posts were me asking for help, so why would I be thanked for that?

I thank everyone who helps me, but you didn't really help, so I didn't. No need to cry about it. You'd think that if you were a teacher you'd be better at helping. If you didn't want to help in the first place you really shouldn't have posted at all.

5. Uhm I have thanked people... I thank everyone who helps me. Maybe they got reset recently, but I know fine well that I've thanked people before. So climb down off that high horse.