Expected Value Calculator
Compute E[X] = Σ x · P(x) from a list of outcomes and probabilities.
What is Expected Value?
The expected value is the long-run average of a random variable: each outcome weighted by its probability, Σ x · P(x). It is not the most likely outcome — a fair die's expected value of 3.5 is a value the die can never show.
How it works
The two lists are paired position by position, each product is accumulated and the total is the expectation. When the probabilities sum to exactly 1 the variance E[X²] − (E[X])² and its square root are reported too; when they do not, the page says the result is a weighted average rather than a true expectation.
- Enter your input. Type or paste your input into the field above — the tool responds instantly.
- Review the result. Output updates live as you type. Everything runs entirely in your browser.
- Copy or download. Use the Copy button to grab the result, or Download to save it as a file.
Examples
Realistic sample
Type or paste any realistic input — the tool computes the result locally and instantly.
Common mistakes
Expecting a server round-trip
Nothing is uploaded — every tool in this category runs entirely in your browser.