Mathematics · University
Poisson zero-event probability · formula reference
λ is the mean count for the entire specified interval, not a rate without a time unit.
Formula
λ is the mean count for the entire specified interval, not a rate without a time unit.
P(X=0) = e^(−λ)
Worked example
A Poisson process has constant rate 0.8 events per minute. What is the probability of no events in 6 minutes? Round the final result to 4 decimal places if needed.
The interval mean is λ = 0.8 × 6. Thus P(X=0) = exp(−λ).
0.0082
Prerequisites and checking
Algebra; calculus or linear algebra as appropriate to the topic. Keep units and rounding consistent. State the model conditions before applying the formula.
Further reading and review references
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