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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Formula

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Poisson Distribution

Formula

`"P"_{"poisson"} = "μ"^("x")*e^(-"μ")/("x"!)`

Example

`"0.180447"=("2")^("3")*e^(-"2")/("3"!)`

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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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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

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< 12 Industrial Parameters Calculators

Binomial Distribution

Go Binomial Distribution = Number of Trials!*(Probability of Success of Single Trial^Specific Outcomes within Trials)*(Probability of Failure of Single Trial^(Number of Trials-Specific Outcomes within Trials))/(Specific Outcomes within Trials!*(Number of Trials-Specific Outcomes within Trials)!)

Normal Distribution

Go Normal Distribution = e^(-(Specific Outcomes within Trials-Mean of Distribution)^2/(2*Standard Deviation of distribution^2))/(Standard Deviation of distribution*sqrt(2*pi))

Learning Factor

Go Learning Factor = (log10(Time for Task 1)-log10(Time for n Tasks))/log10(Number of Tasks)

Poisson Distribution

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

Annual Devaluation Rate

Go Annual Devaluation Rate = (Rate of Return Foreign Currency-Rate of Return USD)/(1+Rate of Return USD)

Crashing

Go Cost Slope = (Crash Cost-Normal Cost)/(Normal Time-Crash Time)

Forecasting Error

Go Forecasting Error = Observed Value at Time t-Smooth Averaged Forecast for Period t

Macroscopic Traffic Density

Go Traffic Density in vpm = Hourly Flow Rate in vph/(Avg. Travel Speed/0.277778)

General Sewing Data

Go GSD = (Man Power*Work Hours)/Target

Traffic Intensity

Go Traffic Intensity = Mean Arrival Rate/Mean Service Rate

Variance

Go Variance = ((Pessimistic Time-Optimistic Time)/6)^2

Reorder Point

Go Reorder Point = Lead Time Demand+Safety Stock

Poisson Distribution Formula

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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