Expected Value
Expected Value is a fundamental concept in probability and statistics that represents the average outcome of a random variable when an experiment is repeated numerous times. It is calculated as the sum of all possible values, each multiplied by the probability of its occurrence.
The formula for expected value (EV) is:
EV = Σ (x * P(x))
where x is a possible outcome and P(x) is the probability of that outcome.
Example 1: Consider a fair six-sided die. The expected value of a roll can be calculated as follows:
- Possible outcomes: 1, 2, 3, 4, 5, 6
- Probabilities: 1/6 for each outcome
EV = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6) = 3.5
Example 2: In a game where you win $10 with a probability of 0.1 and lose $5 with a probability of 0.9:
- Win: $10, Probability: 0.1
- Lose: -$5, Probability: 0.9
EV = (10 * 0.1) + (-5 * 0.9) = 1 – 4.5 = -3.5
This negative expected value indicates that, on average, you would lose $3.50 per game in the long run.