Mathematics · University
Poisson zero-event probability
λ is the mean count for the entire specified interval, not a rate without a time unit.
Method and conditions
λ is the mean count for the entire specified interval, not a rate without a time unit.
P(X=0) = e^(−λ)
Worked examples
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
A Poisson process has constant rate 1 events per minute. What is the probability of no events in 8 minutes? Round the final result to 4 decimal places if needed.
The interval mean is λ = 1 × 8. Thus P(X=0) = exp(−λ).
0.0003
Try it
A Poisson process has constant rate 1.6 events per minute. What is the probability of no events in 8 minutes? Round the final result to 4 decimal places if needed.
A Poisson process has constant rate 1.2 events per minute. What is the probability of no events in 4 minutes? Round the final result to 4 decimal places if needed.
Check your work
Answers and marking notes
- 0
The interval mean is λ = 1.6 × 8. Thus P(X=0) = exp(−λ).
- 0.0082
The interval mean is λ = 1.2 × 4. Thus P(X=0) = exp(−λ).
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