Variance
2026-02-28 09:46 Diff
https://brightchamps.com/en-us/math/data/variance

Variance of Binomial Distribution

The binomial distribution is a discrete probability distribution that represents the number of positive outcomes in a binomial experiment conducted n times, where each trial has only two possible outcomes: success (1) or failure (0). The variance of a binomial distribution, denoted as σ2, is calculated by the formula:

\(σ^2 =np(1−p)\)

Where n is the number of trials, p is the probability of success in each trial, and (1−p) represents the probability of failure. Additionally, np is the mean (expected value) of the binomial distribution, indicating the average number of anticipated successes in n trials.

Variance of Poisson Distribution

The Poisson distribution is a discrete probability distribution used to model the likelihood of a certain number of events occurring within a fixed interval of time or space. It is characterized by the parameter λ (lambda), which represents both the mean and the variance of the distribution. In other words, for a Poisson distribution, the mean and variance are equal, and the formula gives the variance σ2:

\(σ^2 =λ\)

Where λ indicates the average rate of event occurrences in the interval.

Variance of Uniform Distribution

The uniform distribution is a continuous probability distribution in which all outcomes within a specific interval, defined by the lower bound a and the upper bound b, are equally likely. Because of this equal probability for all values in the range, the uniform distribution is also called a rectangular distribution. The variance of a uniform distribution is calculated using the formula:

\(σ^2 = \frac{(b−a)^2}{12}\)

and its mean is given by:

\(Mean = \frac{(a+b)}{2}\)

Where ‘a' is the minimum value and 'b' is the maximum value of the distribution.