# Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: X+Y

Random variables

Random variables Given independent random variables with means and standard deviations as shown, find the mean and standard deviation of: $$X+Y$$

2021-06-02

The mean and standard deviation is as follows:
$$E(X+Y)=E(X)+E(Y)$$
$$=80+12$$
$$=92$$
$$V(X+Y)=V(X)+V(Y)$$
$$SD(X+Y)=\sqrt{V(X)+V(Y)}$$
$$=\sqrt{12^{2}+3^{2}}$$
$$=\sqrt{153}$$
$$=12.3693$$