Random Variables

So far, we have discussed random events (tails coming up on a coin toss) and probability spaces (a coin toss can only be heads or tails because there is nothing else in the probability space), but we have not formally talked about the numerical value of an event. If the number of heads or tails is counted, then the count per se is a random variable, CH for heads and CT for tails. ^[6] "Random variables " is the term we apply to numerical outcomes of events when the value cannot be known in advance of the event and where the value is a number within a range of numbers. When a random event is completed, like tossing a coin 100 times, then the random variables will have specific values obtained by counting, measuring, or observing. In the project world, task durations denoted D with values in hours, days, or weeks and cost figures denoted C with values in dollars, pesos, or euros are two among many random variables project managers will encounter.

If a variable is not a random variable, then it is a deterministic or single-point variable. A deterministic variable has no distribution of values but rather has one and only one value, and there is no uncertainty (risk) as to its measure.

As examples of random and deterministic variables, let us say that we measure cost with variable C and...