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Math Help - Probability density function

  1. #1
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    Probability density function

    Hi, I have this question that I've been struggling with.

    Given D is a random distance with probability density function f_d and expected value \mu, then the sampled distance distribution has probability density function g, where

    g(x)=\frac{xf_d(x)}{\mu}, x \geq 0

    Find the form of the distance probability density function f_d and its expected value \mu if the sample distances are fitted by the probability distance function g(x)=\frac{x^2 e^{-\frac{x}{\alpha}}}{2 \alpha^3}, x \geq 0 and \alpha = 8.1.

    Anyone help will be appreciated. thanks.

    I have tried equating the two g(x) but I keep getting something ridiculous like showing E_d(X) = \mu
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  2. #2
    Moo
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    Hello,

    Do you agree that we have \frac{f_d(x)}{\mu}=\frac{xe^{-x/\alpha}}{2\alpha^3}

    Then f_d(x)=\frac{\mu}{2\alpha^3}\cdot xe^{-x/\alpha}, for any positive x.

    But we want f_d(x) to be a pdf. So its integral over 0 to infinity should be 1. And this computation will give you \mu

    Any further question ?
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