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The formula for the variance of a geometric distribution is given as follows: Var[X] = (1 - p) / p 2
The geometric distribution is the discrete probability distribution that describes when the first success in an infinite sequence of independent and identically distributed Bernoulli trials occurs. Its probability mass function depends on its parameterization and support.
As we have said in the introduction, the geometric distribution is the distribution of the number of failed trials before the first success. The shifted geometric distribution is the distribution of the total number of trials (all the failures + the first success).
Variance of Geometric Distribution. Variance is a measure of dispersion that examines how far data in distribution is spread out in relation to the mean. Var[X] = (1 - p) / p 2. Standard Deviation of Geometric Distribution. The square root of the variance can be used to calculate the standard deviation.
On this page, we state and then prove four properties of a geometric random variable. In order to prove the properties, we need to recall the sum of the geometric series. So, we may as well get that out of the way first. We'll use the sum of the geometric series, first point, in proving the first two of the following four properties.
This page describes the definition, expectation value, variance, and specific examples of the geometric distribution.
The formula for the variance is \(\sigma^2=\left(\frac{1}{p}\right)\left(\frac{1}{p}-1\right)=\left(\frac{1}{0.02}\right)\left(\frac{1}{0.02}-1\right)=2,450\) The standard deviation is \(\sigma=\sqrt{\left(\frac{1}{p}\right)\left(\frac{1}{p}-1\right)}=\sqrt{\left(\frac{1}{0.02}\right)\left(\frac{1}{0.02}-1\right)}=49.5\)
Mean, Variance & Standard Deviation of a Geometric Distribution . For a geometric distribution, μ, the expected number of successes, σ 2, the variance, and σ, the standard deviation for the number of success are given by the formulas, where p is the probability of success and q = 1 – p.
The variance of the distribution is (1-p) / p 2. For example: The mean number of times we would expect a coin to land on tails before it landed on heads would be (1-p) / p = (1-.5) / .5 = 1 .
The variance of a geometric distribution with parameter \(p\) is \(\frac{1-p}{p^2}\). Note that the variance of the geometric distribution and the variance of the shifted geometric distribution are identical, as variance is a measure of dispersion, which is unaffected by shifting.