Poisson Distribution Calculator

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Example

Created on 2024-06-20Asked by Jackson Davis (Solvelet student)

Calculate the probability of

k = 3

events occurring in a given time interval, with an average rate of

\lambda = 2

events per interval, using the Poisson distribution.

Solution

To calculate the probability of

k = 3

events occurring in a given time interval, with an average rate of

\lambda = 2

events per interval, using the Poisson distribution: 1. Use the Poisson probability mass function:

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

2. Substitute

k = 3

and

\lambda = 2

into the formula:

P(X = 3) = \frac{e^{-2} 2^3}{3!}.

3. Calculate the probability:

P(X = 3) = \frac{e^{-2} \cdot 8}{6} \approx 0.180.

Therefore, the probability of

3

events occurring in the given time interval is approximately

0.180

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DefinitionPoisson Distribution is a probability distribution which expresses the possibility of a given number of events happen in a fixed interval of time or space. In this type of distribution, the events are independent and the rate, denoted “λ”, is also constant. For example, it is the type of distribution that can be used to best represent the number of hourly e-mails received assuming that the e-mails are being received at random times and also that the independent events are not received.

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