Track 4 · Probability · Lesson 8 of 9
Expected value and variance of a random payoff
Compute the expected value, variance and standard deviation of a random payoff, and judge when expected value is — and is not — a good basis for a decision.
An electronics shop offers a two-year warranty for 450 SAR. Is it a good deal for the customer, and is it a good business for the shop? The answer depends on the long-run average cost of repairs — the expected value — and on how much the outcome can vary for one customer.
A random variable is a number determined by a chance outcome: the profit from a sales call, the number of claims on a policy, the return on an investment. Its probability distribution lists the possible values and their probabilities, which must add up to 1.
The expected value (also written ) is the probability-weighted average of the values. It is the average you would see per trial if you could repeat the situation many, many times — not necessarily a value that can actually occur.
Included with a Formula Quest membership
It has 7 graded exercises with feedback, hints and worked solutions. After it you will be able to:
- Compute the expected value of a payoff table and explain it as a long-run average
- Compute the variance and standard deviation of a random payoff
- Use expected value to price warranties, insurance and bets
- Explain why expected value alone is not enough for one-off decisions with large losses