When it comes to arithmetic, random variables are not much different than deterministic variables. We can add, subtract, multiply, and divide random variables. For instance, we can define a random variable Z = X + Y, or W = X ². We can transform a random variable into a deterministic variable by calculating its expected value. However, many functional and logical operations on random variables depend on whether or not the variables are mutually exclusive or independent. As examples, the functional operation of expected value does not depend on independence, but the functional operation of variance does.

Similarly, there are operations on statistics that both inherit their properties from deterministic variables and acquire certain properties from the nature of randomness. For instance, the variance of a sum is the sum of variances if the random variables are independent, but the standard deviation of the sum is not the sum of the standard deviations.

Table 2-4 provides a summary of the most important operations for project managers.