Probability Distribution Calculator
Enter the values of a custom discrete distribution with their probabilities to check the distribution and calculate expected value, variance, standard deviation and cumulative probabilities.
See its expected value and spread
Enter your values, or try an example.
Your results and calculation will appear here.
Show calculation
How to use this calculator
- Enter an outcome and its probability on each row; add or remove rows as needed.
- Choose decimal or percent format. Make sure all probabilities total 1 or 100%.
- Calculate to see expected value and spread. Open the calculation for cumulative values.
Worked example: days of sport
x = 0, P(x) = 0.2; x = 1, P(x) = 0.5; x = 2, P(x) = 0.3
Expected value = 1.1
The probability-weighted mean is 1.1; the standard deviation is 0.7 units.
Example calculation
- Probability total = 1.
- E(X) = ΣxP(x) = 1.1.
- Variance = ΣP(x)[x − E(X)]² = 0.49.
- SD = √variance = 0.7.
- F(0) = P(X ≤ 0) = 0.2.
- F(1) = P(X ≤ 1) = 0.7.
Formula & assumptions
E(X) = ΣxP(x); variance = ΣP(x)[x − E(X)]²; F(t) = Σ P(x) for x ≤ t.
- This tool is for discrete outcomes, not a continuous density function.
- Probabilities must be nonnegative and total 1 (or 100%) within 1 × 10⁻¹⁰ in decimal form.
- Inputs are never silently normalized. Duplicate outcomes are allowed and their masses are combined for the CDF.
Sources
Reviewed: October 2026
Common questions
Is this a probability density function calculator?
This calculator accepts a discrete probability mass function. A continuous density requires integration and is not supported here.
What does expected value mean?
It is the probability-weighted mean across outcomes. It need not be an outcome that can occur on a single trial.
Use these tools for mathematical information, not as a substitute for checking assumptions. Read our methodology or disclaimer.