Find expected value from outcome probabilities easily. Review variance, deviation, and validation steps clearly today. Save clean reports and tables for quick probability review.
| Outcome X | Probability P(X) | X × P(X) |
|---|---|---|
| -1 | 0.10 | -0.10 |
| 0 | 0.20 | 0.00 |
| 1 | 0.30 | 0.30 |
| 2 | 0.40 | 0.80 |
| Total | 1.00 | 1.00 |
For this sample distribution, E(X) = 1.00.
Expected value: E(X) = Σ [x × P(x)]
Second moment: E(X²) = Σ [x² × P(x)]
Variance: Var(X) = E(X²) - (E(X))²
Standard deviation: σ = √Var(X)
E(X) is the expected value of a discrete random variable. It gives the long run average outcome. This does not guarantee one exact result. It shows the weighted center of a probability distribution. Each outcome contributes according to its probability. Larger probabilities have more influence. Larger outcomes also have more influence. This makes E(X) useful in planning and analysis.
Expected value is common in mathematics, statistics, finance, games, and risk studies. It helps compare uncertain choices with one summary number. A business can estimate average profit. A student can test probability homework. A researcher can inspect a discrete model quickly. When you combine E(X) with variance, you learn both the average result and the spread around that average.
This E(X) probability calculator accepts multiple outcomes and probabilities in one form. It also checks the total probability. If the values do not sum to one, the normalization option can adjust them. That is useful when your numbers come from estimates, rounded values, or rough inputs. The page also calculates E(X²), variance, and standard deviation. These extra outputs provide deeper probability analysis.
The result section appears below the header and above the form after submission. You can inspect the raw total probability and the used total probability. The working table shows each outcome, each probability, the weighted product, and cumulative probability. This layout makes checking errors much easier. You can confirm that each row was entered correctly. You can also export the result for records, homework notes, or reporting.
Use probabilities between zero and one. Make sure each outcome matches the correct probability. For a complete distribution, the total probability should equal one. Use normalization only when you intentionally want the calculator to rebalance the distribution. For teaching, audit, and documentation work, save the table as CSV or PDF. This supports clear probability review and repeatable calculations.
E(X) represents the expected value of a discrete random variable. It is the weighted average of all possible outcomes, using their probabilities as weights.
Yes. A complete discrete probability distribution should total 1. This calculator can also normalize values when the sum is different, which helps with estimated or rounded inputs.
Yes. Outcomes can be negative, zero, or positive. The calculator multiplies each outcome by its probability, so negative values are handled correctly.
E(X) shows the average outcome. Variance shows how spread out the outcomes are around that average. Standard deviation is the square root of variance.
Blank rows are ignored. Only rows with both an outcome and a probability are used in the calculation.
E(X²) is needed to compute variance. It helps measure the spread of the distribution, not just its center.
Normalize when your probabilities are close to correct but do not total 1 because of rounding or estimation. Do not normalize if the raw totals must remain unchanged for your work.
Yes. You can download the output as a CSV file or save a PDF version. This is useful for homework, audits, and documentation.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.