Mistake Master
A Number for Every Outcome, and the Average No Household Owns
You'll learnwhat a random variable is and what its probability distribution lists, the two requirements that decide whether a table qualifies, how to read at-least and more-than probabilities off the bars without slipping at the boundary, and why the expected value is a balance point and a long-run average rather than a forecast, a mode, or an attainable outcome.
Survey a household and write down its number of pets: that rule is a random variable, and its distribution is a five-line list — 0 pets with probability 0.30, then 0.35, 0.20, 0.10, 0.05. Weight each value by its probability and the average is 1.25 pets, which no household owns and none has to: it is where the histogram balances, pulled between the tall bar at 1 and the tail stretching to 4. Every standard misreading of that number — round it to 1, call it the most likely value, treat it as a forecast for the next door — computes its own wrong answer today, next to the right one. Rounding alone mispredicts a 500-household total by 125 pets. Twelve short steps; press Next for each one.