# Transformation of the exponential distribution

• Aug 22nd 2010, 05:32 PM
chella182
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 $\displaystyle \lambda$. Let $\displaystyle X$ and $\displaystyle Y$ 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 $\displaystyle W=X-Y$. For $\displaystyle w\geq0$, show that

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

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).
• Aug 23rd 2010, 02:21 AM
chella182
I have literally no idea how to sketch that :(
• Aug 24th 2010, 05:15 AM
chella182
Wow, you're a jerk. I love how you asked that question, then presumed you knew the answer...

I thought you meant sketch the $\displaystyle 1-\frac{1}{2}e^{-\lambda w}$ 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?
• Aug 24th 2010, 05:47 AM
chella182
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.
• Aug 24th 2010, 05:58 AM
chella182
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.