Normal

Sum of 2 Independent RVs

Let

• $X\sim N({\mu }_1,{\sigma }_1^2)$
• $Y\sim N({\mu }_2,{\sigma }_2^2)$
• $X,Y$ are independent. Then $X+Y\sim N({\mu }_1+{\mu }_2,{\sigma }_1^2+{\sigma }_2^2)$. https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables