Variance of Geometric Distribution Solution

STEP 0: Pre-Calculation Summary
Formula Used
Variance of Data = Probability of Failure in Binomial Distribution/(Probability of Success^2)
σ2 = qBD/(p^2)
This formula uses 3 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.
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
σ2 = qBD/(p^2) --> 0.4/(0.6^2)
Evaluating ... ...
σ2 = 1.11111111111111
STEP 3: Convert Result to Output's Unit
1.11111111111111 --> No Conversion Required
1.11111111111111 1.111111 <-- Variance of Data
(Calculation completed in 00.004 seconds)
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<Geometric Distribution Calculators

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)
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

Variance of Geometric Distribution Formula

Variance of Data = Probability of Failure in Binomial Distribution/(Probability of Success^2)
σ2 = qBD/(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 Variance of Geometric Distribution?

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

How to calculate Variance of Geometric Distribution using this online calculator? To use this online calculator for Variance of Geometric Distribution, enter Probability of Failure in Binomial Distribution (qBD) & Probability of Success (p) and hit the calculate button. Here is how the Variance of Geometric Distribution calculation can be explained with given input values -> 1.111111 = 0.4/(0.6^2).

FAQ

What is Variance of Geometric Distribution?
Variance of Geometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Geometric distribution, from its mean and is represented as σ2 = qBD/(p^2) or Variance of Data = 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 Variance of Geometric Distribution?
Variance of Geometric Distribution formula is defined as the expectation of the squared deviation of the random variable that follows Geometric distribution, from its mean is calculated using Variance of Data = Probability of Failure in Binomial Distribution/(Probability of Success^2). To calculate Variance of Geometric Distribution, you need Probability of Failure in Binomial Distribution (qBD) & 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.
How many ways are there to calculate Variance of Data?
In this formula, Variance of Data uses 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 -
• Variance of Data = (1-Probability of Success)/(Probability of Success^2)
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