Measure expected outcomes from discrete probability models quickly. See spread, thresholds, and weighted behavior instantly. Make sharper forecasts with clear distribution evidence every time.
Use discrete values and their probabilities to estimate the expected mean and related statistics.
This sample shows a valid discrete probability distribution for expected-value analysis.
| Value (x) | Probability P(x) | x × P(x) |
|---|---|---|
| 0 | 0.1 | 0 |
| 1 | 0.2 | 0.2 |
| 2 | 0.35 | 0.7 |
| 3 | 0.2 | 0.6 |
| 4 | 0.15 | 0.6 |
Mean or expected value: μ = Σ[x × P(x)]
Second moment: E[X²] = Σ[x² × P(x)]
Variance: σ² = E[X²] - μ²
Standard deviation: σ = √(σ²)
Cumulative probability: Sum the probabilities of all qualifying outcomes for your threshold rule.
It represents the expected value of a discrete random variable. The calculator multiplies each outcome by its probability, then adds those weighted contributions.
Yes, a valid probability distribution totals 1. You can also enable normalization, and the calculator will rescale the entered probabilities proportionally.
Yes. Outcomes may be positive, negative, or zero. The calculator still computes the expected mean, variance, and threshold probabilities correctly.
The mean measures the weighted center of outcomes. Variance measures how widely the outcomes spread around that center after accounting for their probabilities.
They help evaluate risk ranges and decision boundaries. You can estimate the chance of staying below, above, or within limits using your distribution.
Yes. It is designed for discrete outcomes with listed probabilities. Continuous distributions usually require density functions and integration instead.
The coefficient of variation becomes undefined because it divides the standard deviation by the mean magnitude. Other statistics still remain available.
Yes. Use the CSV button to save the result table data and the PDF button to print or save a formatted report for sharing.
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.