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 pExpected 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
You have 2 free calculationss remaining
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 |
| 0.83666002653408 |
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
What is the Answer?
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.
Calculates moment number t using the moment generating function
This calculator has 3 inputs.
What 1 formula is used for the Geometric Distribution Calculator?
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
Example calculations for the Geometric Distribution Calculator
Tags:
Add This Calculator To Your Website
