 Linear combination of independent normal random variables

ID: linear-combination-of-independent-normal-random-variables

X_{i} \sim N (μ_{i}, σ_{i}^{2})

\sum_{i} a_{i} X_{i} \sim N (\sum_{i} a_{i} μ_{i}, \sum_{i} a_{i}^{2} σ_{i}^{2}) .

The result follows by multiplying their characteristic functions.

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