Geometric Distribution

Geometric Distribution turns one of probability's most useful ideas into a clean, hands-on app: how many trials does it take to get the first success?

Whether you're a student meeting the topic for the first time, revising for an exam, or a teacher who needs a clear demo, this app keeps the focus on understanding — no clutter, no sign-up, no fuss.

WHAT YOU CAN DO

- Concept — A plain-language explanation of the geometric distribution, its probability mass function, mean, variance, and the famous "memoryless" property, with formulas rendered cleanly.

- Calculator — Set the success probability p and a trial number k, then instantly see P(X = k), P(X ≤ k), P(X > k), the mean, variance, and standard deviation.

- Chart — Visualize the shape of the distribution. Switch between the PMF and CDF and change p to watch the curve and its tail respond in real time.

- Simulation — Run a single sequence of trials until the first success, or run hundreds at once and watch the empirical average close in on the theoretical value 1/p (the law of large numbers in action).

- Examples — Three worked, real-world problems — dice, sales calls, and a coin flip — that show exactly when and how to apply the formula.

WHY THIS DISTRIBUTION MATTERS

The geometric distribution answers questions like "On which attempt will I finally succeed?" It appears in quality control, gaming, sales, reliability testing, and any situation built from repeated independent yes/no trials with a constant chance of success.

Convention used: X is the trial number of the first success, with k = 1, 2, 3, …
P(X = k) = (1 − p)^(k−1) · p
Mean = 1/p Variance = (1 − p)/p²

BUILT TO BE SIMPLE
- Lightweight and fast.
- Clear, distraction-free interface.
- Interactive sliders and live results — learn by doing.

Note: an internet connection is used to display the formulas and ads.

Master the geometric distribution by seeing it, computing it, and simulating it — all in one place.