It is simple to prove that the mean of the sum of random variables is the sum of their means:

e(x1 + x2 + ..xk) = e(x1) + e(x2) + ... + e(xk)

The variance of the sum ofuncorrelatedrandom variables is the sum of their variances:

v(x1+x2+..xk) = v(x1) + v(x2) + .... + v(xk)