Repeated trials and random variables

Check repeated-trial conditions and interpret random variables, distributions, and expected values.

Meaning

A random variable assigns numbers to experimental outcomes. Its distribution describes the probabilities of its values. When there are finitely many possible values, as in this example, its expected value is the sum of each value multiplied by its probability.

Example

For two independent tosses of a fair coin, the number of heads X is 0, 1, or 2, with probabilities and Its expected value is The four outcomes TT, TH, HT, and HH each have probability for independent fair tosses. Two give exactly one head, so P(X=1)= Grouping equal X values in the average gives the expectation formula.An expected value need not occur on every trial. Check whether independence and the same success probability are assumed for repeated trials.

Practice for this concept

Scope and references

Topics

Independent trials, random variables, probability distributions, expected value

Learning goal

Check repeated-trial conditions and interpret random variables, distributions, and expected values.

Helpful background

Connect probability calculations, conditional probability, and independence as needed.