PDF/PMF → CDF Explorer

Sweep x and watch the shaded area under a density (or the sum of a pmf's bars) become the height of the cumulative distribution F(x) — across Normal, Exponential, Uniform, and Binomial.

This interactive probability visualization shows how a cumulative distribution function is built from a density. As you sweep a threshold $x$, the area under a probability density function (or the running sum of a probability mass function's bars) accumulates into the height of the cumulative distribution function $F(x)$ plotted below — turning "probability so far" into a curve you can watch grow.

The relationship is $F(x) = P(X \le x) = \int_{-\infty}^{x} f(t),dt$ for a continuous variable, or a running sum $\sum_{t \le x} p(t)$ for a discrete one. Because it is an accumulation of non-negative probability, the CDF only ever rises, starting at 0 and climbing to 1, and its steepness at any point mirrors how much probability mass sits there — steep where the density peaks, flat in the tails.

Switch between the Normal, Exponential, Uniform, and Binomial distributions to see how each density's shape produces a differently-shaped S-curve, and adjust parameters like the mean to watch the whole picture shift live. Step through the sweep to connect each shaded slice of density to a single point on the CDF. It's a clear, visual way to understand the link between PDFs, PMFs, and CDFs in probability and statistics.