Question

13.9 Show that for the Gaussian probability distribution p(x), the central moments are given by \begin{aligned} E\left(x^{n}\right) &=\int_{-\infty}^{\infty} x^{n} p(x) d x \\ &=\left\{\begin{array}{ll} 0 & \text { for }

n \text { odd } \\ 1 \cdot 3 \cdot 5 \cdots(n-1) \sigma^{n} & \text { for } n \text { even } \end{array}\right. \end{aligned}

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