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Math Help - Exponentially distributed

  1. #1
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    Exponentially distributed

    Let W be the exponentially distributed waiting time in minutes for the next metro train to arrive.
    If P (W < 2) =1/3, compute P (W > 7 | W 5).
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  2. #2
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    Quote Originally Posted by affelix View Post
    Let W be the exponentially distributed waiting time in minutes for the next metro train to arrive.
    If P (W < 2) =1/3, compute P (W > 7 | W 5).
    Solve \int_0^2 \lambda e^{-\lambda x} \, dx = \frac{1}{3} for \lambda.

    \Pr(W > 7 | W \geq 5) = \frac{\int_7^{+\infty} \lambda e^{-\lambda x} \, dx }{\int_5^{+\infty} \lambda e^{-\lambda x} \, dx }.
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  3. #3
    MHF Contributor matheagle's Avatar
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    But P(W>7|W>5)=P(W>2)=1-P(W<2)=2/3

    Who's old now and who is MEMORYLESS?
    I still think that the point of this problem was to highlight the memoryless property.
    That's why I would have assigned it.
    It shows that finding lambda is unnecessary.
    Last edited by matheagle; October 24th 2009 at 09:33 PM.
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  4. #4
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    Quote Originally Posted by matheagle View Post
    But P(W>7|W>5)=P(W>2)=1-P(W<2)=2/3

    Who's old now and who is MEMORYLESS?


    But .... are these rhetorical question ....? I'm tempted to say that the answer to both is you - the latter because you've clearly forgotten what the reaction of a typical student would be to your reply (assuming a student has been exposed to that property of the exponential distribution) .....

    (But you're right, I should have included it as a throw away footnote ....)
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