Geometric Distribution Calculator

The geometric distribution calculator determines the probabilities, mean, variance, and standard deviation of a given distribution.

How to Use the Geometric Distribution Calculator?

First, enter the probability of success on a given trial (p) and the number of failures until the first success (k).
After inputting the values, click the 'Calculate' button to generate probability results.
As a result, the tool returns the simple and cumulative probabilities associated with the geometric distribution. The tool also computes and shows the mean, variance, and standard deviation results.

The probability P(X = k) and P(X < k) can be found using the following formula:

P(X = k) = (1 - p)^k × p

P(X < k) = P(X = 1) + P(X = 2) + P(X = 3) + ... + P(X = k)

The mean, variance, and standard deviation for the geometric distribution are calculated using the following formulas:

						
									Mean (μ) =  
									1 - p
p

									Variance (σ2) =  
									1 - p
p2

									SD (σ) =  
									√
									1 - p
p2

Where,
p = Probability of Success,
k = Number of Trials,
SD = Standard Deviation.