Calculate geometric distribution probabilities, mean, variance, and cumulative probabilities. Perfect for statistics and probability analysis.
Enter a value between 0 and 1 (e.g., 0.25 for 25%)
Enter a positive integer
If you have a 20% chance of making a free throw in basketball:
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.
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.
The geometric distribution has one parameter: p (probability of success on each trial). The probability of failure is q = 1 - p.
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.
The variance of a geometric distribution is σ² = (1-p)/p², which measures the spread of the distribution around the mean.
Yes, theoretically a geometric distribution can take on any positive integer value, though the probability decreases as the number of trials increases.
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