Recent content by Avinto

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    Integral of Gaussian function, for squared x

    Ok, I see what you mean about the variance, the definition of \phi on the wiki page assumes \sigma=1. Using \sigma=1, my calculation did evaluate to one, which is where I must have gotten that assumption from. I redid my calculations with including \sigma, and realized I made a silly error in...
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    Integral of Gaussian function, for squared x

    Thank you for your suggestions. Ray, I will attempt to work it out using your way later today, and see how it goes. Orodruin, I have had a go at your method, but have not had much luck. t = x^2 \Gamma(z) = \int_0^{∞} t^{z-1} exp(-t) dt \Gamma(3) = \int_0^{∞} t^{3-1} \exp(-t)...
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    Integral of Gaussian function, for squared x

    Homework Statement I am trying to compute an integral, as part of the expected value formula (using a Gaussian PDF) \int_{-∞}^{∞} (x)^2 p(x) dx Where p(x) is the Gaussian probability density function: \frac{1}{\sigma \sqrt(2 \pi)} \exp(\frac{-x^2}{2 \sigma^2}) My aim after this is...