Part One: Probability

What is a Random Variable?

A random variable is a rule for turning the outcomes of trials of experiments into numbers. Let RV denote the random variable; then

RV: Outcome Þ Number ; or

Number = RV(OUTCOME).

The rule RV takes each outcome and produces a numeric result. Mathematically, a random variable is a function that maps a domain of outcomes into a range of numeric results:

domain(RV) = {the set of experimental outcomes}

range(RV) = {a range of numbers}

The choice of random variable depends on the nature of information to be obtained from the experiment. The choice of random variable is not unique, and in most designs there will be a random variable for each item of information.