Definition: RandomVariable

Definition: Random (or Stochastic) Variable

  1. A random variable is a function that associates a number with each outcome of the sample space of a chance experiment.

  2. Let \(S\) be the sample space of an experiment. A random variable is a function from \(S\) to the real line. Random variables are usually denoted by a capital letter. Individual observed values of a random variable are usually denoted by the corresponding lower case letter. Example: We toss a fair coin three times. Let \(X\) be the stochastic variable that counts the number of heads. If we conduct this experiment once and see we had 2 heads in that individual observation of the experiment, we write \(x = 2\). We could ask the questions, “What is the probability that \(X = 2\)?” or “What is the probability that \(X = x\)?”

Source: These definitions are from Probability & Statistics with R by Akritas and Foundations of Statistics with R by Speegle & Clair.