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Math Help - Transformation of the exponential distribution

  1. #1
    Senior Member chella182's Avatar
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    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).
    Attached Thumbnails Attached Thumbnails Transformation of the exponential distribution-2007-2008.pdf  
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  2. #2
    Senior Member chella182's Avatar
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    I have literally no idea how to sketch that
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  3. #3
    Senior Member chella182's Avatar
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    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?
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  4. #4
    Senior Member chella182's Avatar
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    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.
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  5. #5
    Senior Member chella182's Avatar
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    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.
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