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Math Help - Finding the median given a p.d.f.

  1. #1
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    Post Finding the median given a p.d.f.

    Let X have the p.d.f. f (x) = c * e^(Abs(x)) for -1<= x < 1 (please note the absolute value marks.

    I determined c to be 1/(2e-2)
    but how do you calculate the median of X. I believe it has something to do with the 50th percentile but I'm not sure how to make that calculation. Thank you for your time.
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  2. #2
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    Quote Originally Posted by Intsecxtanx View Post
    Let X have the p.d.f. f (x) = c * e^(Abs(x)) for -1<= x < 1 (please note the absolute value marks.

    I determined c to be 1/(2e-2)
    but how do you calculate the median of X. I believe it has something to do with the 50th percentile but I'm not sure how to make that calculation. Thank you for your time.
    First find c by

    \int_{-1}^1 c\times e^{|x|}~dx = 1

    Then once you have c

    find a such that \int_{a}^1 c\times e^{|x|}~dx = 0.5
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  3. #3
    MHF Contributor matheagle's Avatar
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    This is a symmetric distribution about 0, so 0 better be the median.
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