Using the geometric distribution with a success probability of 0.3, ca ·

02 Jun 2024, 00:00

Using the geometric distribution with a success probability of 0.3, ca Image to Crop

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

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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.

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?

distributionvalue range for a variableeventa set of outcomes of an experiment to which a probability is assigned.geometric distributionDiscrete probability distribution
μ = 1/p; σ2 = 1 - p/p2meanA statistical measurement also known as the averageprobabilitythe 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 Outcomesstandard deviationa measure of the amount of variation or dispersion of a set of values. The square root of variancevarianceHow far a set of random numbers are spead out from the mean

Using the geometric distribution with a success probability of 0.3, ca

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 * 0.74P(x = 5) = 0.3 * 0.2401 P(x = 5) = 0.072 Calculate the mean : Calculate the variance 2: