Poisson Distribution Calculator

✖Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution.ⓘ Mean of Distribution [μ]			+10% -10%
✖Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.ⓘ Specific Outcomes within Trials [x]			+10% -10%

✖The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period.ⓘ Poisson Distribution [P_poisson]

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Poisson Distribution Solution

STEP 0: Pre-Calculation Summary

Formula Used

Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!)
P_poisson = μ^(x)*e^(-μ)/(x!)
This formula uses 1 Constants, 3 Variables

Constants Used

e - Napier's constant Value Taken As 2.71828182845904523536028747135266249

Variables Used

Poisson Distribution - The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period.
Mean of Distribution - Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution.
Specific Outcomes within Trials - Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.

STEP 1: Convert Input(s) to Base Unit

Mean of Distribution: 2 --> No Conversion Required
Specific Outcomes within Trials: 3 --> No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

P_poisson = μ^(x)*e^(-μ)/(x!) --> 2^(3)*e^(-2)/(3!)

Evaluating ... ...

P_poisson = 0.180447044315484

STEP 3: Convert Result to Output's Unit

0.180447044315484 --> No Conversion Required

FINAL ANSWER

0.180447044315484 ≈ 0.180447 <-- Poisson Distribution

(Calculation completed in 00.004 seconds)

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Credits

Created by Suman Ray Pramanik

Indian Institute of Technology (IIT), Kanpur

Suman Ray Pramanik has created this Calculator and 50+ more calculators!

Verified by Akshada Kulkarni

National Institute of Information Technology (NIIT), Neemrana

Akshada Kulkarni has verified this Calculator and 900+ more calculators!

< Industrial Parameters Calculators

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Poisson Distribution Formula

LaTeX Go

Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!)
P_poisson = μ^(x)*e^(-μ)/(x!)

What is Poisson probability distribution?

The Poisson probability distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period. The Poisson distribution is used to describe the distribution of rare events in a large population. Poisson distribution describes the distribution of binary data from an infinite sample. Thus it gives the probability of getting r events in a population.

How to Calculate Poisson Distribution?

Poisson Distribution calculator uses Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!) to calculate the Poisson Distribution, The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period. Poisson Distribution is denoted by P_poisson symbol.

How to calculate Poisson Distribution using this online calculator? To use this online calculator for Poisson Distribution, enter Mean of Distribution (μ) & Specific Outcomes within Trials (x) and hit the calculate button. Here is how the Poisson Distribution calculation can be explained with given input values -> 0.180447 = 2^(3)*e^(-2)/(3!).

FAQ

What is Poisson Distribution?

The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period and is represented as P_poisson = μ^(x)*e^(-μ)/(x!) or Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!). Mean of Distribution is the long-run arithmetic average value of a random variable having that distribution & Specific Outcomes within Trials are the number of times a certain outcome takes place within a given set of trials.

How to calculate Poisson Distribution?

The Poisson distribution is the discrete probability distribution of the number of events occurring in a given time period, given the average number of times the event occurs over that time period is calculated using Poisson Distribution = Mean of Distribution^(Specific Outcomes within Trials)*e^(-Mean of Distribution)/(Specific Outcomes within Trials!). To calculate Poisson Distribution, you need Mean of Distribution (μ) & Specific Outcomes within Trials (x). With our tool, you need to enter the respective value for Mean of Distribution & Specific Outcomes within Trials and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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