Expected Value Calculator
Calculate expected value and variance for discrete probability distributions
About this calculator
The Expected Value Calculator computes the expected value (mean) and variance for discrete probability distributions. This tool helps statisticians, students, and analysts determine the average outcome and measure of spread for random variables. Expected value represents the long-run average result, while variance indicates how much outcomes deviate from this average. It's essential for risk assessment, decision-making under uncertainty, and probability analysis in finance, insurance, and research applications.
How to use
Enter your discrete values and their corresponding probabilities in the input fields. Ensure all probabilities sum to 1.0 for a valid distribution. Click calculate to instantly compute the expected value, variance, and standard deviation for your probability distribution.
Frequently asked questions
What is expected value in probability?
Expected value is the average outcome of a random variable over many trials, calculated by multiplying each possible value by its probability and summing the results.
How do I interpret variance results?
Variance measures how spread out the values are from the expected value. Higher variance indicates greater variability and uncertainty in outcomes.
Do probabilities need to sum to exactly 1?
Yes, for a valid probability distribution, all probabilities must sum to exactly 1.0, representing 100% of all possible outcomes.