<-- Enter Total Occurrences (n)
<-- Enter probability of success (p)
<-- OPTIONAL Enter moment number t for moment calculation

Using the geometric distribution with a success probability of 0.3, calculate the probability of exactly 1 success on trial number 5

Expected Frequency (skip if you are calculating probability):

Expected frequency = n x p
Expected frequency = 5 x 0.3
Expected frequency = 1.5

Determine our formula:
P(x = n) = p * (1 - p)(n - 1)

Plug in our values:
P(x = 5) = 0.3 * (1 - 0.3)(5 - 1)
P(x = 5) = 0.3 * 0.74
P(x = 5) = 0.3 * 0.2401
P(x = 5) = 0.072

Now calculate the Mean (μ), Variance (σ2), and Standard Deviation (σ)

Calculate the mean μ:
 μ  = 1 p

 μ  = 1 0.3

μ = 3

Calculate the variance σ2:
 σ2  = 1 - p p2

 σ2  = 1 - 0.3 0.32

 σ2  = 0.7 0.09

σ2 = 7.7778

Calculate the standard deviation σ:
σ  =  √σ2
σ  =  √7.7778
σ = 2.7889

Calculate skewness:

 Skewness  = 2 - p √1 - p

 Skewness  = 2 - 0.3 √1 - 0.3

 Skewness  = 1.7 √0.7

 Skewness  = 1.7 0.83666

Skewness = 2.0318886358685

Calculate Kurtosis:

Kurtosis = 6 + p2/(1 - p)
Kurtosis = 6 + 0.32/(1 - 0.3)
Kurtosis = 6 + 0.09/0.7
Kurtosis = 6 + 0.12857142857143
Kurtosis = 6.1285714285714

P(x = 5) = 0.072
How does the Geometric Distribution Calculator work?
Free Geometric Distribution Calculator - Using a geometric distribution, it calculates the probability of exactly k successes, no more than k successes, and greater than k successes as well as the mean, variance, standard deviation, skewness, and kurtosis.
Calculates moment number t using the moment generating function
This calculator has 3 inputs.

What 1 formula is used for the Geometric Distribution Calculator?

P(x = n) = p * (1 - p)(n - 1)

For more math formulas, check out our Formula Dossier

What 7 concepts are covered in the Geometric Distribution Calculator?

distribution
value range for a variable
event
a set of outcomes of an experiment to which a probability is assigned.
geometric distribution
Discrete probability distribution
μ = 1/p; σ2 = 1 - p/p2
mean
A statistical measurement also known as the average
probability
the likelihood of an event happening. This value is always between 0 and 1.
P(Event Happening) = Number of Ways the Even Can Happen / Total Number of Outcomes
standard deviation
a measure of the amount of variation or dispersion of a set of values. The square root of variance
variance
How far a set of random numbers are spead out from the mean