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Variance of Negative Binomial Distribution Calculator

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✖Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials.ⓘ Number of Success [N_Success]			+10% -10%
✖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%

✖Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.ⓘ Variance of Negative Binomial Distribution [σ²]

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Variance of Negative Binomial Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2)
σ² = (N_Success*q_BD)/(p^2)
This formula uses 4 Variables

Variables Used

Variance of Data - Variance of Data is the expectation of the squared deviation of the random variable associated with the given statistical data from its population mean or sample mean.
Number of Success - Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials.
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

Number of Success: 5 --> No Conversion Required
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

σ² = (N_Success*q_BD)/(p^2) --> (5*0.4)/(0.6^2)

Evaluating ... ...

σ² = 5.55555555555556

STEP 3: Convert Result to Output's Unit

5.55555555555556 --> No Conversion Required

FINAL ANSWER

5.55555555555556 ≈ 5.555556 <-- Variance of Data

(Calculation completed in 00.004 seconds)

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< Binomial Distribution Calculators

Standard Deviation of Binomial Distribution

LaTeX Go Standard Deviation in Normal Distribution = sqrt(Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution)

Mean of Negative Binomial Distribution

LaTeX Go Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success

Variance of Binomial Distribution

LaTeX Go Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution

Mean of Binomial Distribution

LaTeX Go Mean in Normal Distribution = Number of Trials*Probability of Success

Variance of Negative Binomial Distribution Formula

LaTeX Go

Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2)
σ² = (N_Success*q_BD)/(p^2)

What is Negative Binomial Distribution?

The Negative Binomial 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 given number of successes to occur.
The probability of success in each trial is denoted as "p" and the number of successes is denoted as "r". The probability mass function of the negative binomial distribution is given by: P(X = k) = (k-1+r)C(r-1) *(p^r)*((1-p)^(k-r))

The Negative Binomial Distribution is a generalization of the geometric distribution, which corresponds to the case when r=1. It is used in modeling the number of failures before a given number of successes in a sequence of Bernoulli trials.

How to Calculate Variance of Negative Binomial Distribution?

Variance of Negative Binomial Distribution calculator uses Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2) to calculate the Variance of Data, Variance of Negative Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Negative Binomial distribution, from its mean. Variance of Data is denoted by σ² symbol.

How to calculate Variance of Negative Binomial Distribution using this online calculator? To use this online calculator for Variance of Negative Binomial Distribution, enter Number of Success (N_Success), Probability of Failure in Binomial Distribution (q_BD) & Probability of Success (p) and hit the calculate button. Here is how the Variance of Negative Binomial Distribution calculation can be explained with given input values -> 5.555556 = (5*0.4)/(0.6^2).

FAQ

What is Variance of Negative Binomial Distribution?

Variance of Negative Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Negative Binomial distribution, from its mean and is represented as σ² = (N_Success*q_BD)/(p^2) or Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2). Number of Success is the number of times that a specific outcome which is set as the success of the event occurs in a fixed number of independent Bernoulli trials, 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 Variance of Negative Binomial Distribution?

Variance of Negative Binomial Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Negative Binomial distribution, from its mean is calculated using Variance of Data = (Number of Success*Probability of Failure in Binomial Distribution)/(Probability of Success^2). To calculate Variance of Negative Binomial Distribution, you need Number of Success (N_Success), Probability of Failure in Binomial Distribution (q_BD) & Probability of Success (p). With our tool, you need to enter the respective value for Number of Success, 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.

How many ways are there to calculate Variance of Data?

In this formula, Variance of Data uses Number of Success, Probability of Failure in Binomial Distribution & Probability of Success. We can use 2 other way(s) to calculate the same, which is/are as follows -

Variance of Data = Number of Trials*Probability of Success*Probability of Failure in Binomial Distribution
Variance of Data = Number of Trials*Probability of Success*(1-Probability of Success)

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