Poisson Distribution

Poisson Distribution

Poisson Distribution describes the number of events occurring in a fixed time interval or region of opportunity.

Poisson Distribution is a discrete probability distribution.

Poisson Distribution (Google Image)

Notation

If X follows a poisson distribution with a mean of, lambda (λ) occurrences per interval or rate. We write it as.

Notation

Probability Mass Function (PMF)

Probability Mass Function (PMF) (Google Image)

Probability Mass Function (PMF)

Cumulative Distribution Function (CDF)

Cumulative Distribution Function (CDF) (Google Image)

Cumulative Distribution Function (CDF)

Combine Independent Variables

For any combined independents variables.

Combine Independent Variables

Mean

Lambda (λ) is the mean number of events within a given interval of time or space.

Mean

If the mean is large then the Poisson distribution is approximately a normal distribution.

Variance

In poisson distribution variance is equals to mean.

Variance

Standard Deviation

Standard Deviation for a poisson distribution is given by.

Standard Deviation

Conditions

• The events must be independent of each other. The occurrence of one event must not affect the probability another event will occur.
• The average rate, events per time is constant.
• Two events cannot occur at the same time.

When?

Poisson distribution is used when we know the rate or interval in which the event occurs. Here are some examples —

• We know the percentage of defective pieces in production
• People arriving every hour.
• Number of phone calls in a day.

I hope this article provides you with a basic understanding of Poisson Distribution.

If you have any questions or if you find anything misrepresented please let me know.

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