Discrete random variables – expectation as the long-run average

MathematicsProbabilityAges 17–18

Build the probability distribution table of a discrete random variable in a real-world scenario (a dice game with a prize, the number of correct guesses on a multiple-choice quiz, the number of defective items in a batch), then compute the expectation, variance and standard deviation, and run thousands of simulated trials to watch the experimental mean converge on the expectation — and so decide whether the game favours the player.