Explain the rules 3 and 4 in sum of several random variables.

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.