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Math Help - how to tranform between functions in integral

  1. #1
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    how to tranform between functions in integral

    Suppose x is normal variable x~N(a,b)
    and y=160*x^2
    I need calculate ∫f(y)d(y)
    f(y) is the density function of y
    how can I write it as an integral of x since we know x's distribution, I mean use the density function of x to substitute the original integral

    Thank you!
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  2. #2
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    Quote Originally Posted by aegea View Post
    Suppose x is normal variable x~N(a,b)
    and y=160*x^2
    I need calculate ∫f(y)d(y)
    f(y) is the density function of y
    how can I write it as an integral of x since we know x's distribution, I mean use the density function of x to substitute the original integral

    Thank you!
    Read this: Noncentral chi-square distribution - Wikipedia, the free encyclopedia
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    Quote Originally Posted by mr fantastic View Post

    Thank you. Is there a way I don't need to deal with chi-square dist since it's more difficult to get the integral.

    Sorry for not saying it clear earlier. The original question was calculate E(y), since E(y)=∫yf(y)d(y)
    can I just use E(y)=E(160x^2)=
    ∫160x^2f(x)d(x)
    and f(x) is the density function of normal

    Thank you
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  4. #4
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    Quote Originally Posted by aegea View Post
    Thank you. Is there a way I don't need to deal with chi-square dist since it's more difficult to get the integral.

    Sorry for not saying it clear earlier. The original question was calculate E(y), since E(y)=∫yf(y)d(y)
    can I just use E(y)=E(160x^2)=∫160x^2f(x)d(x)
    and f(x) is the density function of normal

    Thank you
    Note that ∫x^2 f(x) dx = E(X^2).

    Now note also that Var(X) = E(X^2) - [E(X)]^2 => E(X^2) = Var(X) + [E(X)]^2. And since you're told X ~ N(a,b) you know Var(X) and E(X) ....
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