Sums of Random Variables:

Rule 3: \(\mu_{x+y} = \mu_{x} + \mu_{y}\)

The rule 3 represents the mean values of the two random variables X and Ycan be added.

Rule 2: \(\sigma_{x+y}=\sqrt{\sigma_{x}^{2}+\sigma_{y}^{2}}\)

The rule 4 represents the standard deviation value of the random variable X+Y of the two random variables X and Y, the variance of the variables XYand Ycan be added if the variables are independent.