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Math Help - Normal Distribution PDF conversion

  1. #1
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    Normal Distribution PDF conversion

    A) Find the pdf of W = X^2 when X ~ N(10,9)

    B) Suppose that X ~ N(E(X)), Var(X)). Find the pdf of Y = e^x

    Not sure how to do these. Any help?
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  2. #2
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    Quote Originally Posted by wolverine21 View Post
    A) Find the pdf of W = X^2 when X ~ N(10,9)

    B) Suppose that X ~ N(E(X)), Var(X)). Find the pdf of Y = e^x

    Not sure how to do these. Any help?
    A) Similar to the one asked here: http://www.mathhelpforum.com/math-he...functions.html

    B) Get the cdf of Y: G(y) = \Pr(Y < y) = \Pr(e^X < y) = \Pr(X < \ln y) = \, ....

    Then the pdf of Y is g(y) = \frac{dG}{dy}.

    Note:  G(y) = \int_{-\infty}^{\ln y} f(x) \, dx \Rightarrow \frac{dG}{dy} = \frac{1}{y} \, f(\ln y) (using the Fundamental Theorem of Calculus and the chain rule) where f(x) is the pdf of X.
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