Standard Deviation of Geometric Distribution Calculator

✖Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Failure in Binomial Distribution [q_BD]			+10% -10%
✖Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.ⓘ Probability of Success [p]			+10% -10%

✖Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.ⓘ Standard Deviation of Geometric Distribution [σ]

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Standard Deviation of Geometric Distribution

Formula

`"σ" = sqrt("q"_{"BD"}/("p"^2))`

Example

`"1.054093"=sqrt("0.4"/(("0.6")^2))`

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Standard Deviation of Geometric Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2))
σ = sqrt(q_BD/(p^2))
This formula uses 1 Functions, 3 Variables

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Standard Deviation in Normal Distribution - Standard Deviation in Normal Distribution is the square root of expectation of the squared deviation of the given normal distribution following data from its population mean or sample mean.
Probability of Failure in Binomial Distribution - Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials.
Probability of Success - Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.

STEP 1: Convert Input(s) to Base Unit

Probability of Failure in Binomial Distribution: 0.4 --> No Conversion Required
Probability of Success: 0.6 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

σ = sqrt(q_BD/(p^2)) --> sqrt(0.4/(0.6^2))

Evaluating ... ...

σ = 1.05409255338946

STEP 3: Convert Result to Output's Unit

1.05409255338946 --> No Conversion Required

FINAL ANSWER

1.05409255338946 ≈ 1.054093 <-- Standard Deviation in Normal Distribution

(Calculation completed in 00.004 seconds)

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< 6 Geometric Distribution Calculators

Geometric Distribution

Go Geometric Probability Distribution Function = Probability of Success in Binomial Distribution*Probability of Failure^(Number of Independent Bernoulli Trials)

Standard Deviation of Geometric Distribution

Go Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2))

Variance of Geometric Distribution

Go Variance of Data = Probability of Failure in Binomial Distribution/(Probability of Success^2)

Variance in Geometric Distribution

Go Variance of Data = (1-Probability of Success)/(Probability of Success^2)

Mean of Geometric Distribution given Probability of Failure

Go Mean in Normal Distribution = 1/(1-Probability of Failure in Binomial Distribution)

Mean of Geometric Distribution

Go Mean in Normal Distribution = 1/Probability of Success

Standard Deviation of Geometric Distribution Formula

Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2))
σ = sqrt(q_BD/(p^2))

What is Geometric Distribution?

A Geometric Distribution is a probability distribution for a discrete random variable that describes the number of Bernoulli trials (experiments with only two possible outcomes, such as success or failure) that must be conducted in order for a success to occur.
The probability of success in each trial is denoted as "p" and is a parameter of the distribution. The probability of the k-th trial being the first success is given by the probability mass function: P(X=k) = ((1-p)^(k-1))*p

The Geometric Distribution is a special case of the negative binomial distribution. It is used in modeling the number of failures before the first success in a sequence of Bernoulli trials.

How to Calculate Standard Deviation of Geometric Distribution?

Standard Deviation of Geometric Distribution calculator uses Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2)) to calculate the Standard Deviation in Normal Distribution, Standard Deviation of Geometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Geometric distribution, from its mean. Standard Deviation in Normal Distribution is denoted by σ symbol.

How to calculate Standard Deviation of Geometric Distribution using this online calculator? To use this online calculator for Standard Deviation of Geometric Distribution, enter Probability of Failure in Binomial Distribution (q_BD) & Probability of Success (p) and hit the calculate button. Here is how the Standard Deviation of Geometric Distribution calculation can be explained with given input values -> 1.054093 = sqrt(0.4/(0.6^2)).

FAQ

What is Standard Deviation of Geometric Distribution?

Standard Deviation of Geometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Geometric distribution, from its mean and is represented as σ = sqrt(q_BD/(p^2)) or Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2)). Probability of Failure in Binomial Distribution is the probability of a specific outcome not occurring in a single trial of a fixed number of independent Bernoulli trials & Probability of Success is the probability of a specific outcome occurring in a single trial of a fixed number of independent Bernoulli trials.

How to calculate Standard Deviation of Geometric Distribution?

Standard Deviation of Geometric Distribution formula is defined as the square root of expectation of the squared deviation of the random variable that follows Geometric distribution, from its mean is calculated using Standard Deviation in Normal Distribution = sqrt(Probability of Failure in Binomial Distribution/(Probability of Success^2)). To calculate Standard Deviation of Geometric Distribution, you need Probability of Failure in Binomial Distribution (q_BD) & Probability of Success (p). With our tool, you need to enter the respective value for Probability of Failure in Binomial Distribution & Probability of Success and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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