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Math Help - How to integrate this integral?

  1. #1
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    How to integrate this integral?

    \int_{0}^{\infty}x^2e^{-x^2/(2\theta^2)}dx
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  2. #2
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    Hello,

    Note that this integral is half \int_{\mathbb{R}} x^2 e^{-x^2/2\sigma^2} ~dx

    but then you can recognize e^{-x^2/2\sigma^2} as nearly the pdf of a random variable Z following N(0,\sigma^2)

    Try to find what \sigma^2=E[Z^2] is, in terms of an integral and compute that integral.
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