Linear combination of independent normal random variables
= Linear combination of independent normal random variables
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}