Practice Problem: compute the zero-th order moment of a Gaussian random variable


A random variable X has the following probability density function:

$ f_X (x) = \frac{1}{\sqrt{2\pi} 3 } e^{\frac{-(x-3)^2}{18}} . $

Compute the moment of order two of that random variable. In other words, compute

$ E \left( X^2 \right) . $


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