# Poisson Distribution

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## Definition of 'Poisson Distribution'

The Poisson distribution is a discrete probability distribution that expresses the probability of a given number of events occurring in a fixed interval of time or space. It is named after the French mathematician SimÃ©on Denis Poisson, who first described it in 1837.

The Poisson distribution is often used to model the number of events that occur in a fixed interval of time or space when the average number of events is known. For example, it can be used to model the number of phone calls that a call center receives in a given hour, or the number of defects that occur in a manufactured product.

The Poisson distribution is a special case of the binomial distribution. The binomial distribution describes the probability of a given number of successes in a sequence of independent experiments, each of which has a constant probability of success. The Poisson distribution is a limiting case of the binomial distribution when the number of experiments is large and the probability of success is small.

The Poisson distribution is a very versatile distribution that can be used to model a wide variety of phenomena. It is often used in queuing theory, reliability engineering, and quality control.

The Poisson distribution is defined by the following formula:

```

P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}

```

where:

* X is the number of events that occur in a fixed interval of time or space.

* ? is the average number of events that occur in the interval.

* x is the number of events that we are interested in.

The Poisson distribution has the following properties:

* The mean and variance of the Poisson distribution are both equal to ?.

* The Poisson distribution is skewed to the right.

* The Poisson distribution approaches a normal distribution as ? gets larger.

The Poisson distribution is a very important distribution in statistics. It is used to model a wide variety of phenomena, and it has a number of useful properties.

The Poisson distribution is often used to model the number of events that occur in a fixed interval of time or space when the average number of events is known. For example, it can be used to model the number of phone calls that a call center receives in a given hour, or the number of defects that occur in a manufactured product.

The Poisson distribution is a special case of the binomial distribution. The binomial distribution describes the probability of a given number of successes in a sequence of independent experiments, each of which has a constant probability of success. The Poisson distribution is a limiting case of the binomial distribution when the number of experiments is large and the probability of success is small.

The Poisson distribution is a very versatile distribution that can be used to model a wide variety of phenomena. It is often used in queuing theory, reliability engineering, and quality control.

The Poisson distribution is defined by the following formula:

```

P(X = x) = \frac{\lambda^x e^{-\lambda}}{x!}

```

where:

* X is the number of events that occur in a fixed interval of time or space.

* ? is the average number of events that occur in the interval.

* x is the number of events that we are interested in.

The Poisson distribution has the following properties:

* The mean and variance of the Poisson distribution are both equal to ?.

* The Poisson distribution is skewed to the right.

* The Poisson distribution approaches a normal distribution as ? gets larger.

The Poisson distribution is a very important distribution in statistics. It is used to model a wide variety of phenomena, and it has a number of useful properties.

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Copyright © 2004-2023, MyPivots. All rights reserved.