📊 Probability Distributions Explorer

Adjust parameters of Normal, Binomial, Poisson, Exponential, and Uniform distributions. Compare PDF vs CDF, overlay a second distribution, and inspect mean, variance, and key quantiles.

Distribution 1

Mean μ 0 Std dev σ 1.0

Trials n 20 Probability p 0.50

Rate λ 3.0

Rate λ 1.0

Min a 0 Max b 5

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Statistics

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P(x ≤ cursor)–

Distributions

Normal (Gaussian): The "bell curve". Arises from sums of independent random variables (Central Limit Theorem). Parametrized by mean μ and std σ.
Binomial: Number of successes in n independent yes/no trials each with probability p. Discrete distribution.
Poisson: Number of events in a fixed interval when events occur at constant rate λ. Approximates Binomial when n is large and p is small.
Exponential: Waiting time between Poisson events. Memoryless property: P(T > s+t | T > s) = P(T > t).
Uniform: Equally likely values on [a, b]. Maximum entropy distribution for bounded support.

How to Use

Select a distribution type and slide the parameters — the curve updates instantly
Toggle PDF / CDF to switch between density and cumulative functions
Enable Compare Distribution 2 to overlay a second distribution and see differences visually
Move your mouse over the canvas — one value and its CDF probability are shown at cursor

Did You Know?

The Central Limit Theorem says that the sum (or average) of many independent random variables converges to a Normal distribution, regardless of the original distribution — as long as mean and variance are finite. This is why the Normal distribution appears so often in nature and statistics.