11.5 Random variables and decisions
Unit 11 · Probability and counting
Ideas in this lesson
Expected value
Weight each possible outcome by its probability, then add. Expected value is a long-run average.
Binomial mean and spread
A binomial mean is trial count times success probability; its variance also includes the failure probability.
Binomial variance
A binomial variance is the trial count times the success probability times the failure probability. Standard deviation is its positive square root.
Fair games
A game is fair when the expected net gain is zero. Subtract the entry cost from any payout.
At least one
Use the complement of zero successes when direct enumeration of several success counts is less efficient.
Original MathLab worked examples and fresh practice. Free with an account.