Means and standard deviations.

Question

Given three independent random variables $X_k$, the means and standard deviations respectively are $X_1 = (A, X)$, $X_2 = (B, Y)$, $X_3 = (C,Z)$.

(1)What is the mean of their sum?
(2)What is the deviation of their sum?

Is it just as simple as (1) $= A + B+ C$ and (2) $= X + Y + Z$

Answer 1

$E(X_1 + X_2 + X_3) = A + B + C$ because of linearity of the expectation operator.

$V(X_1 + X_2 + X_3) = X^2 + Y^2 + Z^2$

where

$V(.)$ denotes the variance.