Maths and Computing:

X ~ Po(λ)

The Poisson distribution is a discrete distribution used to calculate the probability that a given number of events occur over a given interval.

Example

X ~ Po(2): The probability that x events occur in an interval where the average number of events is 2.

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Conditions

• Each event is independent
• Events occur at a constant average rate (λ)
• Events cannot occur at the same time

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Formulae

x: the number of events occurring

P(X = x) =	e-λλx x!
E(X) = λ
VAR(X) = λ

Enter the parameters for the Poisson distribution:

Parameter: λ

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This calculator does the following

• Displays the statistics for the defined distribution
• Calculates the probabilities for a given value of x
• Calculates the inverse for a given probability
• Calculates the values for a hypothesis test given the significance level: H₀, H₁, the critical region, probability of a type I error and the probability of a type II error given the actual parameter.
• Calculates the values for a hypothesis test given the critical region: H₀, H₁, the test size, the test power for the actual parameter or the power table if no parameter is specified.
• Displays a table of probabilities for the distribution