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 * 0.7

^{4} P(x = 5) = 0.3 * 0.2401

P(x = 5) = **0.072**

Now calculate the Mean (μ), Variance (σ

^{2}), and Standard Deviation (σ)

__Calculate the mean μ:__ μ =

**3** __Calculate the variance σ__^{2}:

σ

^{2} =

**7.7778** __Calculate the standard deviation σ:__ σ = √

σ^{2} σ = √

7.7778 σ =

**2.7889**## Calculate skewness:

Skewness = | 2 - 0.3 |

| √1 - 0.3 |

Skewness = | 1.7 |

| 0.83666002653408 |

Skewness =

**2.0318886358685**## Calculate Kurtosis:

Kurtosis = 6 + p

^{2}/(1 - p)

Kurtosis = 6 + 0.3

^{2}/(1 - 0.3)

Kurtosis = 6 + 0.09/0.7

Kurtosis = 6 + 0.12857142857143

Kurtosis =

**6.1285714285714**

##### 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; σ^{2} = 1 - p/p^{2} - 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

##### Example calculations for the Geometric Distribution Calculator

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