Random variables and expected value
Give every outcome of two dice a number, find the probability of values of that number, work out the average of a die, and decide how much a game is worth per throw.
- UK: Year 13
- France: grade 10
- Afghanistan: grade 12
- Syria: grade 12
- Palestine: grade 11
- Russia: grade 11
Guide
This studio follows Afghan grade 12 chapter 7 (the probability distribution function and expected value) and the UK A-level discrete random variables.
A random variable X gives a number to every outcome, for example the total of two dice. Its distribution lists each value of X with its probability. The expected value E(X) is each value times its probability, added up: the long-run average.
Common mistakes worked on here: counting (1, 3) and (3, 1) as one outcome, thinking the totals are equally likely, using only the equal value when asked for "at least", taking the middle of the list for the average, and forgetting the loss in a game.