Expected Value Calculator
Calculate E(X) = sum of x * P(x) for discrete outcomes.
This tool is for informational and educational purposes only. It is not a substitute for professional financial, medical, legal, or engineering advice. See Terms of Service.
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Enter your outcomes in the first field and their corresponding probabilities in the second field, both comma-separated. The probabilities should sum to 1. The calculator instantly computes the expected value by multiplying each outcome by its probability and summing.
About This Calculator
The expected value is the long-run average result of a random variable over many repetitions. It is central to decision theory, gambling analysis, insurance, and any field where you weigh outcomes by their likelihood. The formula is E(X) = sum of xi * P(xi).
Frequently Asked Questions
What if my probabilities do not sum to 1?
For a valid probability distribution, all probabilities must sum to 1. The calculator will warn you if your probabilities do not sum correctly.
Can expected value be negative?
Yes. If outcomes include negative values (like losses), the expected value can be negative, indicating a net loss on average.
How is expected value different from the mean?
For a probability distribution, the expected value IS the mean. For raw data without probabilities, the arithmetic mean assumes equal probabilities for each observation.