Mean of Negative Binomial Distribution Calculator

✖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%

✖Mean in Normal Distribution is the average of the individual values in the given statistical data which follows normal distribution.ⓘ Mean of Negative Binomial Distribution [μ]

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Mean of Negative Binomial Distribution

Formula

`"μ" = ("N"_{"Success"}*"q"_{"BD"})/"p"`

Example

`"3.333333"=("5"*"0.4")/"0.6"`

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Mean of Negative Binomial Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success
μ = (N_Success*q_BD)/p
This formula uses 4 Variables

Variables Used

Mean in Normal Distribution - Mean in Normal Distribution is the average of the individual values in the given statistical data which follows normal distribution.
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

μ = (N_Success*q_BD)/p --> (5*0.4)/0.6

Evaluating ... ...

μ = 3.33333333333333

STEP 3: Convert Result to Output's Unit

3.33333333333333 --> No Conversion Required

FINAL ANSWER

3.33333333333333 ≈ 3.333333 <-- Mean in Normal Distribution

(Calculation completed in 00.004 seconds)

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Home » Math » Probability and Disribution » Distribution » Binomial Distribution » Mean of Negative Binomial Distribution

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< 8 Binomial Distribution Calculators

Binomial Probability Distribution

Go Binomial Probability = (C(Total Number of Trials,Number of Successful Trials))*Probability of Success in Binomial Distribution^Number of Successful Trials*Probability of Failure^(Total Number of Trials-Number of Successful Trials)

Standard Deviation of Negative Binomial Distribution

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

Standard Deviation of Binomial Distribution

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

Mean of Negative Binomial Distribution

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

Variance of Negative Binomial Distribution

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

Variance of Binomial Distribution

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

Variance in Binomial Distribution

Go Variance of Data = Number of Trials*Probability of Success*(1-Probability of Success)

Mean of Binomial Distribution

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

Mean of Negative Binomial Distribution Formula

Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success
μ = (N_Success*q_BD)/p

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 Mean of Negative Binomial Distribution?

Mean of Negative Binomial Distribution calculator uses Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success to calculate the Mean in Normal Distribution, Mean of Negative Binomial Distribution formula is defined as the long-run arithmetic average of individual values of the random variable that follows Negative Binomial distribution. Mean in Normal Distribution is denoted by μ symbol.

How to calculate Mean of Negative Binomial Distribution using this online calculator? To use this online calculator for Mean 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 Mean of Negative Binomial Distribution calculation can be explained with given input values -> 3.333333 = (5*0.4)/0.6.

FAQ

What is Mean of Negative Binomial Distribution?

Mean of Negative Binomial Distribution formula is defined as the long-run arithmetic average of individual values of the random variable that follows Negative Binomial distribution and is represented as μ = (N_Success*q_BD)/p or Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability 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 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 Mean of Negative Binomial Distribution?

Mean of Negative Binomial Distribution formula is defined as the long-run arithmetic average of individual values of the random variable that follows Negative Binomial distribution is calculated using Mean in Normal Distribution = (Number of Success*Probability of Failure in Binomial Distribution)/Probability of Success. To calculate Mean 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 Mean in Normal Distribution?

In this formula, Mean in Normal Distribution uses Number of Success, Probability of Failure in Binomial Distribution & Probability of Success. We can use 1 other way(s) to calculate the same, which is/are as follows -

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

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