Probability Distribution Plotter

Plot PMF and CDF for a binomial distribution.

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What This Calculator Does

Plot PMF and CDF for a binomial distribution.

It combines Trials (n), Success Probability (p) to estimate Mean, Variance.

Formula & Method

Core equations: Binomial PMF/CDF:

P(X=k)=\binom{n}{k}p^k(1-p)^{n-k},\quad F(k)=\sum_{i=0}^{k}P(X=i)

Notation used in the formulas: $R$ = Mean; $x_{1}$ = Trials (n); $x_{2}$ = Success Probability (p).

Method summary: inputs are normalized to consistent units, core equations are evaluated, then secondary values are derived and rounded for display.

Use this calculator for quick scenario analysis. Start with baseline values, change one driver at a time, and compare how sensitive the results are to each input shown above.

Reference Book

Introduction to Mathematical Statistics

Global Edition

Robert V. Hogg, Joseph McKean, and Allen T. Craig · Pearson

A standard reference for probability distributions, estimation, hypothesis testing, regression, and ANOVA.

View Book

Inputs Used

Trials (n): Used directly in the calculation.
Success Probability (p): Used directly in the calculation.

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