How to Find Expected Value
The expected value (EV) is a fundamental concept in probability and statistics that represents the average outcome of a random variable over numerous trials. To calculate the expected value, follow these steps:
Step 1: Define the Random Variable
Identify the random variable for which you want to calculate the expected value. This could be anything from the roll of a die to the expected return on an investment.
Step 2: Determine Possible Outcomes
List all possible outcomes of the random variable. For example, when rolling a six-sided die, the possible outcomes are 1, 2, 3, 4, 5, and 6.
Step 3: Assign Probabilities
Assign a probability to each outcome. Ensure that the total probabilities sum to 1. For a fair die, each outcome has a probability of 1/6.
Step 4: Multiply Outcomes by Their Probabilities
For each outcome, multiply the outcome value by its assigned 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 5: Sum the Results
Add all the products from the previous step. This sum is the expected value. For the die example, the expected value would be:
(1/6 + 2/6 + 3/6 + 4/6 + 5/6 + 6/6) = 21/6 = 3.5
No related topics found.
