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Math Help - Variance for Functions

  1. #1
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    Variance for Functions

    I have never seen anyone do this but has anyone defined the variance for a countinous function f(x) on interval [a,b]?
    I used "reasonable" definition to get:
    \frac{1}{b-a}\int^b_a[f(x)-\= x]^2dx
    where,
    \=x is the average value, thus,
    \=x=\frac{1}{b-a}\int^b_a f(x)dx
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  2. #2
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    Quote Originally Posted by ThePerfectHacker
    I have never seen anyone do this but has anyone defined the variance for a countinous function f(x) on interval [a,b]?
    I used "reasonable" definition to get:
    \frac{1}{b-a}\int^b_a[f(x)-\= x]^2dx
    where,
    \=x is the average value, thus,
    \=x=\frac{1}{b-a}\int^b_a f(x)dx
    Yes, usually in the following context:

    Let X be a random variable with pdf p(x), and f be a function defined
    on the event space \Omega of X. Then Y=f(X), is a random variable with mean:

    \mu _Y = \int_{\Omega} f(x)p(x) dx,

    and variance:

    \sigma _Y^2 =\int_{\Omega}(f(x)- \mu_Y)^2 p(x) dx

    RonL
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  3. #3
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    CaptainBlack, I can see you are very knowledgable in Statistics.
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by ThePerfectHacker
    CaptainBlack, I can see you are very knowledgable in Statistics.

    Mebee

    RonL
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