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Normal distribution

If $X_i\sim N(\mu_i,\sigma_i^2)$ are <independent random variables>, then
$$
\sum_i a_iX_i\sim N\left(\sum_i a_i\mu_i,\sum_i a_i^2\sigma_i^2\right).
$$
The result follows by multiplying their <characteristic function>[characteristic functions].

= Gaussian distribution
{synonym}

Linear combination of independent normal random variables

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codex/gaussian-distribution

Linear combination of independent normal random variables

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Linear combination of independent normal random variables

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