Quick guide
How to use this calculator
- Enter the observations, probabilities, model parameters, or summary statistics requested by the visible labels.
- Keep every value on the same scale and confirm that the selected sampling relationship, distribution, and tail convention match the question you are investigating.
- Read the result together with its assumptions and interpretation. Statistical output summarizes uncertainty under a model; it does not repair biased data or establish causation.
Calculation method
How the discrete probability distribution calculator works
E(X)=Σxp; Var(X)=Σx²p−E(X)²; interval probability sums masses whose outcomes lie inside the bounds.
The table defines a discrete random variable; expected value is a long-run average and need not be a possible single outcome.
Worked example
Discrete Probability Distribution example
Outcomes 0 and 10 with probabilities 0.7 and 0.3 have mean 3, variance 21, and standard deviation about 4.583.
E(X)=Σxp; Var(X)=Σx²p−E(X)²; interval probability sums masses whose outcomes lie inside the bounds.
Supported inputs
Precision and limits
Model and design
Lists must align, probabilities must be between zero and one and total one, and interval bounds are inclusive.
Numerical scope
Inputs use double-precision numerical methods with guarded domains. Datasets accept up to 10,000 finite plain-decimal values. Extremely large parameters or probabilities deep in a numerical tail may require specialist statistical software.
Interpretation
The table defines a discrete random variable; expected value is a long-run average and need not be a possible single outcome.
Decision boundary
The calculator does not validate how data were collected, diagnose dependence or bias, choose a scientifically meaningful effect, or replace review by a qualified statistician for consequential research, medical, regulatory, safety, or policy decisions.
Privacy
Entered values and calculated results stay in this browser and are not sent to an analytics service.
Continue calculating