Poisson Distribution Mean and Variance
In the Poisson distribution, both the mean (average) and variance are equal and are denoted by the parameter λ (lambda). This property of equal mean and variance is a distinctive characteristic of the Poisson distribution and simplifies its statistical analysis.
Poisson Distribution Mean
Mean of a Poisson distribution is also known as Poisson Distribution expected value or average of the distribution and is represented by “E[X]” or “λ” (lambda). This means that the mean for poison distribution is equal to the parameter i.e., λ. Mathematically, this equation is represented as follows:
E[X] = λ
where,
- E[X] is Mean of Poisson’s Distribution
- λ is Parameter of Distribution
- X is Random Variable following a Poisson distribution
Other than this, we have one more formula for the mean of expectation of the distribution that is:
Mean = λ = np
where,
- n is Number of Trails
- p is Probability of Success
Poisson Distribution Variance
Variance is the measure of the spread or dispersion of the random variable around its mean. For Poisson Distribution, variance is equal to the parameter λ (lambda).
Thus, the variance of a Poisson distribution can be expressed as:
Var(X) = λ
where,
- Var(X) is the variance of the Poisson-distributed random variable X
- λ is the parameter of the Poisson distribution
Poisson Distribution | Definition, Formula, Table and Examples
Poisson Distribution is one of the types of discrete probability distributions like binomial distribution in probability. It expresses the probability of a given number of events occurring in a fixed interval of time.
Poisson distribution is a type of discrete probability distribution that determines the likelihood of an event occurring a specific number of times (k) within a designated time or space interval. This distribution is characterized by a single parameter, λ (lambda), representing the average number of occurrences of the event.
In this article, we will discuss the Poisson Distribution including its definition, Poisson Distribution formula, Poisson Distribution examples, and properties of Poisson Distribution in detail.
Table of Content
- What is Poisson Distribution?
- Poisson Distribution Definition
- Poisson Distribution Formula
- Poisson Distribution Table
- Poisson Distribution Characteristics
- Poisson Distribution Graph
- Poisson Distribution Mean and Variance
- Poisson Distribution Mean
- Poisson Distribution Variance
- Standard Deviation of Poisson Distribution
- Probability Mass Function of Poisson Distribution
- Difference between Binomial and Poisson Distribution
- Poisson Distribution Examples
- Poisson Distribution Practice Problems