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Math Help - Exponential distributions

  1. #1
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    Exponential distributions

    let X have an exponential pfd with B=500. so f(x)=(1/500)exp(-x/500) with x from 0 to infinity.
    a. compute P(X>500)
    b. compute the conditional probability

    again thanks!
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  2. #2
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    Quote Originally Posted by Dubulus View Post
    let X have an exponential pfd with B=500. so f(x)=(1/500)exp(-x/500) with x from 0 to infinity.
    a. compute P(X>500)
    b. compute the conditional probability

    again thanks!
    a. This is the application of a basic definition you should be familiar with:

    \Pr(X > 500) = \int_{500}^{+\infty} \frac{1}{500} \, e^{-x/500} \, dx.

    Do the integration. Get the answer.

    b. The question is incomplete. What's the given event??
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  3. #3
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    a. thats what my book says, but somehow i remember a way of figuring this out without doing an integral...
    b. thats exactly what i thought, unfortunately it says nothing further than that. any ideas what it could possibly mean?
    keep in mind this book is absolutely terrible
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    Quote Originally Posted by Dubulus View Post
    a. thats what my book says, but somehow i remember a way of figuring this out without doing an integral...
    b. thats exactly what i thought, unfortunately it says nothing further than that. any ideas what it could possibly mean?
    keep in mind this book is absolutely terrible
    a. Unless you have memorised that \Pr(X > \mu) = e^{-1} for an exponential distribution, you have to integrate.

    b. Obviously the given event could be anything. The question is incomplete and as such is impossible to answer.
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