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Math Help - problem with distribution function

  1. #1
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    problem with distribution function

    hi there, this problem has really confused me, could someone please help me. the distribution function of random variable A is given, and i must find a distribution function of new random variable B=1/A.
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  2. #2
    MHF Contributor matheagle's Avatar
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    what is your question?
    First of all that distribution function is wrong.
    It's ok that F(x)=0 when x is less than 1
    and F(x)=1 when x is greater than 2
    BUT it cannot be x from 1 to 2.
    MAYBE your instructor meant F(x)=x-1, since F cannot exceed 1.
    This says that F(1.5)=1.5 which means that P(X\le 1.5)=1.5 which is a no-no.

    BUT in order to transform, I use calc 1

    f_B(b)=f_A(a)\left|{dA\over dB}\right|

    which can easily be proved by differentiating the cdfs, which was the approach of your teacher.
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  3. #3
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    Quote Originally Posted by matheagle View Post
    what is your question?
    First of all that distribution function is wrong.
    you're right, it was my mistake, i confused it with function which is defined in [0,1], in [1,2] it would be x-1. with this function all stuff works. thanks
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