Geometric Distribution Calculator

Calculate geometric distribution probabilities, mean, variance, and cumulative probabilities. Perfect for statistics and probability analysis.

Calculator

Enter a value between 0 and 1 (e.g., 0.25 for 25%)

Enter a positive integer

Geometric Distribution Formula

PMF: P(X = n) = p × q^(n-1)
Mean: μ = 1/p
Variance: σ² = (1-p)/p²
Where: p = probability of success, q = 1-p

Example

If you have a 20% chance of making a free throw in basketball:

  • • P(X = 1) = 0.20 (20% chance of making it on first try)
  • • P(X = 2) = 0.16 (16% chance of making it on second try)
  • • Expected number of attempts: 1/0.20 = 5 attempts

Frequently Asked Questions

What is a geometric distribution?

A geometric distribution is a probability distribution that describes the number of trials needed to get the first success in a series of independent Bernoulli trials, where each trial has the same probability of success.

When do we use geometric distribution?

Geometric distribution is used when we want to find the probability of getting the first success on the nth trial, such as the number of attempts needed to make a free throw in basketball or the number of calls needed to get a response.

What are the parameters of geometric distribution?

The geometric distribution has one parameter: p (probability of success on each trial). The probability of failure is q = 1 - p.

How do you calculate the mean of geometric distribution?

The mean (expected value) of a geometric distribution is μ = 1/p, which represents the expected number of trials needed to get the first success.

What is the variance of geometric distribution?

The variance of a geometric distribution is σ² = (1-p)/p², which measures the spread of the distribution around the mean.

Can geometric distribution have infinite values?

Yes, theoretically a geometric distribution can take on any positive integer value, though the probability decreases as the number of trials increases.