Geometric Distribution Calculator
Enter a success probability and trial number to compute PMF, CDF, mean, variance, and standard deviation for the geometric distribution.
Parameters
Must be between 0 and 1 (exclusive).
Trial on which first success may occur (k ≥ 1).
Distribution Statistics
- Mean (Expected value)
- —
- Variance
- —
- Standard Deviation
- —
Results for k = 3
PMF — P(X = k)
—
Probability of first success on trial k
CDF — P(X ≤ k)
—
Probability of first success by trial k
P(X > k)
—
Probability first success after trial k
Formula
—
P(X = k) = (1 − p)^(k−1) × p
Probability Table
First 15 trials| k | P(X = k) | P(X ≤ k) |
|---|
Summary
Enter a success probability and trial number to compute PMF, CDF, mean, variance, and standard deviation for the geometric distribution.
How it works
- Enter the probability of success p (a value between 0 and 1).
- Enter the trial number k (the trial on which the first success occurs).
- The calculator instantly shows P(X = k) (PMF) and P(X ≤ k) (CDF).
- Distribution stats — mean, variance, and standard deviation — update automatically.
- Use the table to explore probabilities across multiple values of k at once.
Use cases
- Finding the probability that the first success happens on exactly the k-th trial.
- Quality control: modeling the number of inspections until the first defect is found.
- Reliability engineering: estimating the number of attempts before the first failure.
- Game design: calculating the chance a player first succeeds on a given turn.
- Sales modeling: probability a cold call converts on the n-th attempt.
- Network transmission: probability of the first successful packet delivery.
Frequently Asked Questions
Last updated: 2026-06-13 ·
Reviewed by Nham Vu