What is the expected value?

What is the expected value?

• A. The weighted average of all possible outcomes
• B. The most probable outcome
• C. The maximum possible payoff
• D. The minimum possible payoff

Answer: (A)

The expected value is the long-run average outcome you would expect if you could repeat the random process many times. It is calculated as a weighted average of all possible results, with each result weighted by its probability. In a discrete case, you multiply each payoff by its probability and sum those products. For a fair six-sided die, the expected value is (1+2+3+4+5+6)/6 = 3.5, meaning the average payoff you'd approach over many rolls. This is not the same as the most probable result, nor the maximum or minimum payoff.

The expected value is the long-run average outcome you would expect if you could repeat the random process many times. It is calculated as a weighted average of all possible results, with each result weighted by its probability. In a discrete case, you multiply each payoff by its probability and sum those products. For a fair six-sided die, the expected value is (1+2+3+4+5+6)/6 = 3.5, meaning the average payoff you'd approach over many rolls. This is not the same as the most probable result, nor the maximum or minimum payoff.