I know how to calculate mean and variance of some given numbers but I have trouble computing them for probability distributions especially when it is a continuous probability distribution. For example, can you show me how to calculate mean and variance of Gaussian distribution?
2026-04-03 22:59:35.1775257175
Mean and Variance of probability distributions
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$$E[X]=\int xf_X(x)\mathrm dx\qquad E[X^2]=\int x^2f_X(x)\mathrm dx$$ $$\mathrm{var}(X)=E[X^2]-E[X]^2$$