The probability-eating monster

Imagined by Shobhana Stoyanov and implemented by Claude
Department of Statistics, UC Berkeley ·

Type in a probability mass function and watch the CDF walk along the x-axis. The CDF is a probability-eating function: it goes along the x-axis, swallowing all the probability it finds and growing bigger. So at each x, it has eaten everything up to and including what it finds at x. Eventually it eats all the available probability and cannot grow any bigger.

x = −2 F(x) = P(X ≤ x) = 0 Empty CDF has nothing inside

Probability distribution

xf(x) = P(X = x)Eaten
Total = 1

Probabilities can be fractions like 1/3 or decimals like 0.25. Repeated x values are combined.

What you're seeing

The monster's height
F(x) = P(X ≤ x): all the probability it has eaten so far. It gets bigger as F grows.
The red blocks
Probability waiting at each possible value. A block's height is f(x), so it fills the jump in the CDF.
○ and ●
At each jump, the open circle is the height just before x and the filled dot is F(x). The CDF is right-continuous.
The two ends
Far to the left the CDF is empty (F = 0). Past the largest value it is full grown (F = 1).