Expected Value Calculator
Calculate the average outcome of a random event.
Input Data
Enter the possible values of the random variable and their corresponding probabilities. Separate each value and probability with a comma.
Possible outcomes, comma-separated.
Probabilities for each value, comma-separated.
Expected Value:
Calculation Breakdown
| Value (xᵢ) | Probability (P(xᵢ)) | xᵢ * P(xᵢ) |
|---|---|---|
| Total Expected Value |
Formula
$$E(X) = \sum_{i=1}^{n} x_i P(x_i)$$
Understanding Expected Value
Expected Value (or Mean) predicts the average outcome over many trials. For a discrete random variable, it's the sum of each outcome multiplied by its probability.
Formula: $$E(X) = \sum_{i=1}^{n} x_i P(x_i)$$, where \( x_i \) are values and \( P(x_i) \) are probabilities.
Use: Used in risk assessment, finance, and games to estimate average results. Helps in making informed decisions by predicting long-term averages.
Learn more about Expected Value on Wikipedia.