Visualize normal, binomial, Poisson, exponential, chi-squared, and 15+ distributions. Adjust parameters and see PDF/CDF update.
Choose from 15 or more distribution families - normal, binomial, Poisson, exponential, chi-squared, and others - then adjust the parameters (mean and standard deviation, trials and success probability, rate, degrees of freedom) and watch the curve redraw instantly. The plot shows the probability density or mass function, with the cumulative distribution function available as a second view, so you can read probabilities such as P(X <= 1) directly. The thing people trip on: for continuous distributions the curve's height is a density, not a probability - it can exceed 1 - so probabilities come only from areas under the curve.
A concrete input and expected output from the current implementation.
Input
Normal distribution; mean 0, standard deviation 1; read the curve at x = 1, plus the band between x = -1 and x = 1.
Expected output
PDF at x = 1: about 0.2420. CDF at x = 1: 0.84134, so P(X <= 1) is about 0.8413. By symmetry, CDF at x = -1 is 0.15866, and the band between -1 and 1 holds 0.84134 - 0.15866 = 0.68268, about 0.6827 of the total area - the 68% of the 68-95-99.7 rule.
For the standard normal, the CDF at x is the area under the bell curve to the left of x. Phi(1) = 0.84134, and subtracting Phi(-1) = 0.15866 gives the middle band of 0.68268, matching the 68-95-99.7 rule. The 0.2420 at x = 1 is the density, which is not itself a probability.
Each family carries its own controls: normal takes a mean and standard deviation, binomial takes trials and success probability, Poisson takes a rate, chi-squared takes degrees of freedom. Changing any control recomputes the curve immediately. Continuous families draw a smooth density curve; discrete families draw bars whose heights are actual probabilities, and the axes rescale to keep the whole shape visible.
The CDF at any point is the area under the PDF to the left of that point, or the sum of bar heights up to that point for discrete families. Moving the evaluation point slides a shaded region on the PDF and updates the CDF readout in lockstep. The CDF always starts at 0, ends at 1, and never decreases - a quick sanity check on any reading.
For continuous distributions the curve is a probability density, not a probability. Its height has no direct meaning; only the area under it between two values is a probability, and that area always lies between 0 and 1. A density exceeds 1 whenever the distribution is narrow, such as an exponential with a large rate. The CDF view is where probabilities appear directly.
For standard textbook setups, yes: the underlying definitions follow conventional references, and this is a reasonable check against tables. Still, verify the parameterization - rate versus mean for the exponential, for instance - and the tool's rounding before treating agreement as proof. When in doubt, compare against two independent sources rather than one.
The example and behavioral notes were checked against the browser implementation. Standards and primary references below define the relevant format, formula, or platform behavior.
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