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Math Help - Transformations of random variables with the exponential distribution

  1. #1
    Senior Member chella182's Avatar
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    Transformations of random variables with the exponential distribution

    Just posted a similar thread, but I'm not sure if you're allowed multiple questions in one thread (sorry if you are!)

    X is exponentially distributed with parameter \lambda. For the random variable Y=\frac{1}{X}
    i) State the range of values Y can take.
    ii) Obtain the distribution function of Y, F_{Y}(y).
    iii) Obtain the probability density function of Y, f_{Y}(y).
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  2. #2
    MHF Contributor matheagle's Avatar
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    First of all I would like to know how you write your exponential distribution.
    And the range is (0,\infty)

    F_Y(y)=P(Y\le y)=P(1/X\le y)=P(X\ge 1/y)=\lambda\int_{1/y}^{\infty}e^{-x\lambda} dx
    Last edited by matheagle; November 26th 2009 at 03:37 PM.
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  3. #3
    Senior Member chella182's Avatar
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    \lambda e^{-\lambda x} is how we use the exponential distribution.
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