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Math Help - Chi-squared expected value

  1. #1
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    Chi-squared expected value

    Hello, I need to get the expected value of a chi-squared distribution with one degree of freedom, using the following formula with the pdf:

    E[Y]=\int_0^\infty y f(y) dy

    So, E[Y]= \int_0^\infty y \frac{1}{\sqrt{2 \pi y}} e^{-y/2}dy = \int_0^\infty \frac{\sqrt{y}}{\sqrt{2 \pi}} e^{-y/2}dy

    I have no idea how to deal with that integral. I know that there are easier ways to do it, but I am supposed to solve it using this integral. Thanks in advance.
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  2. #2
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    Quote Originally Posted by akolman View Post
    Hello, I need to get the expected value of a chi-squared distribution with one degree of freedom, using the following formula with the pdf:

    E[Y]=\int_0^\infty y f(y) dy

    So, E[Y]= \int_0^\infty y \frac{1}{\sqrt{2 \pi y}} e^{-y/2}dy = \int_0^\infty \frac{\sqrt{y}}{\sqrt{2 \pi}} e^{-y/2}dy

    I have no idea how to deal with that integral. I know that there are easier ways to do it, but I am supposed to solve it using this integral. Thanks in advance.
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