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  1. #1
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    integral of probability density function




    Hi,

    I apologize for the almost certainly stupid question. I'm sure somebody must have asked it before but I have searched and cannot find an aswer.

    The normal probability density function is everywhere greater than zero. When the standard deviation of the distribution is 0.1, the pdf at x=0 is 3.98942.

    Since the pdf is never negative, how can the integral of the pdf be equal to one? It seems to me that it must be > 3.98942.

    Obviously I have misunderstood something about probability density functions! Please help me out if you can.

    Regards,

    M

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    The integral of f: R -> R represents area, not height. Viewed as a sum of rectangles A1 + ... + An, with Ai = hi*wi, the height (h) or width (w) can be larger than 1, but their product cannot be. That is, hi > 1 OR wi > 1, for some i, but hi*wi = Ai < 1, for all i.

    An example: f(x) = 2, for 0 < x < 1/2. This is a valid probability density (uniform with parms. a = 0, b = 1/2) and f(x) > 1 for any x.

  3. #3
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    Thanks zmogggggg,

    Ok I think I understand. That is very helpful!

    Cheers!

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