Expected Value Calculator
Calculate the expected value, a key concept in probability theory, representing the average outcome of a random variable over many trials.
Enter Outcomes and Probabilities
For each possible outcome, enter its value and corresponding probability. Click "Add Outcome" for more entries.
Result
Breakdown
The expected value is calculated as the sum of each outcome multiplied by its probability. Here's a detailed breakdown:
| Outcome | Probability | Weighted Value |
|---|---|---|
| Total Expected Value |
What is Expected Value?
Expected value, also known as expectation, is a fundamental concept in probability theory. It represents the average value you would expect to obtain if you repeated an experiment or random process a large number of times. For a discrete random variable, it's calculated by multiplying each possible outcome by its probability and summing these products. It's widely used in decision making, risk assessment, and finance to predict long-term average outcomes. For example, in games of chance, the expected value helps determine if a game is fair or advantageous.
- Formula: E(X) = Σ [xᵢ * P(xᵢ)], where xᵢ are outcomes and P(xᵢ) are their probabilities.
- Use Cases: Gambling, insurance, investment decisions, and statistical analysis.
- Learn More: Wikipedia on Expected Value