Poisson Distribution Calculator
Calculate P(X=k) for the Poisson distribution with rate parameter λ. Models the probability of k events in a fixed interval.
How to Use the Poisson Distribution Calculator
- Enter the average rate λ (events per interval).
- Enter the number of events k.
- Click Calculate to find the probability P(X = k).
クイックリファレンス
| 変換元 | 変換先 |
|---|---|
| λ=2, k=0 | P ≈ 0.1353 |
| λ=2, k=2 | P ≈ 0.2707 |
| λ=5, k=5 | P ≈ 0.1755 |
| λ=10, k=10 | P ≈ 0.1251 |
| Mean = Var = λ | Key property |
使用例
- •Estimating server request rates for capacity planning.
- •Predicting defect counts in manufacturing.
- •Modeling rare event occurrences in insurance.
計算式
P(X=k) = (λ^k × e^(−λ)) / k!. Mean = λ. Variance = λ.
よくある質問
What is the Poisson distribution?
A probability distribution that models the number of events occurring in a fixed interval of time or space, given a known average rate.
What does λ represent?
Lambda (λ) is the average number of events per interval.
When to use Poisson?
For rare events: server requests per minute, typos per page, accidents per month.