# Expected Value Calculator

> Calculate the expected value, variance, and standard deviation of a discrete random variable distribution.

**URL:** https://www.calculatoranswers.com/expected-value-calculator
**Category:** Education

## Quick Answer

Calculate the expected value E(X) of a discrete probability distribution. Enter values and their probabilities to find the mean, variance, and standard deviation.

## Definition

An expected value calculator computes the theoretical mean (expected value) of a discrete random variable. By summing the product of each possible outcome and its respective probability, the tool evaluates the long-term average outcome of a random process. It also validates that all probabilities sum to exactly 1.0 and reports the distribution's variance and standard deviation.

## How to Use

1. **Add distribution rows** — Specify the value (x_i) and probability (p_i) for each outcome.
2. **Validate probabilities** — Ensure the sum of all probabilities equals exactly 1.0.
3. **Read expected value** — Review the computed E(X), variance, and standard deviation with the summation breakdown.

## Disclaimer

This calculator provides estimates for educational and planning purposes. Always consult a qualified professional for specific advice on financial, medical, legal, or other regulated decisions.

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