How to Calculate Expected Value
The expected value (EV) is a fundamental concept in probability and statistics that provides a measure of the center of a probability distribution. It represents the average outcome of a random variable over a large number of trials. To calculate the expected value, follow these steps:
Step 1: Identify Possible Outcomes
List all possible outcomes of the random variable. For example, if you're rolling a die, the possible outcomes are 1, 2, 3, 4, 5, and 6.
Step 2: Assign Probabilities
Assign a probability to each outcome. For a fair die, each outcome has a probability of 1/6.
Step 3: Multiply Outcomes by Their Probabilities
For each outcome, multiply the value of the outcome by its probability. For example:
- 1 × (1/6) = 1/6
- 2 × (1/6) = 2/6
- 3 × (1/6) = 3/6
- 4 × (1/6) = 4/6
- 5 × (1/6) = 5/6
- 6 × (1/6) = 6/6
Step 4: Sum the Results
Add all the results from Step 3 to get the expected value:
EV = (1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6) = 21/6 = 3.5
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