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Math Help - Hard Probability Question

  1. #1
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    Hard Probability Question

    Hi Guys, I have quite a hard question, I am attaching 2 picture, one of the question and 1 of my attempt to solve the first part, I must have done something wrong, either from probability point of view or calculus...

    any ideas for "a" and "b" (which I have no clue about) will be appreciated.


    Thank you !!

    Hard Probability Question-attempt.jpg Hard Probability Question-question.jpg
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  2. #2
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    a)

    i have not checked your solution in detail, but i would point out that

    e^{20-lnr} = e^{20}e^{-lnr} = e^{20}r^{-1}

    i think that makes your integral a bit more do-able


    b) The profit (X) appears to be

    X = 1000 - \frac{1000}{T}

    (Note that the minimum value of T is 20, so the minimum value of X is 950)

    Start by finding the CDF of X
    P(X<x) = P(1000-\frac{1000}{T} < x )

    P(X<x) = P(\frac{1000}{T} > 1000 -  x )

    P(X<x) = P(\frac{T}{1000} < \frac{1}{1000 -  x} )

    P(X<x) = P(T < \frac{1000}{1000 -  x} )


    P(X<x) = F_T(\frac{1000}{1000-x})

    P(X<x) = 1-exp \left( 20 - \frac{1000}{1000-x} \right)  , x \geq 950

    Assuming my algebra was correct (check!), differentiate to obtain the desity of x.
    Last edited by SpringFan25; August 3rd 2010 at 08:13 AM.
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  3. #3
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    thank you!! I did what you suggested, I think I got the correct result !
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  4. #4
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    woo

    i also edited my original post while you were typong that, has more info on part b now.
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