如何计算Poisson Distribution
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The Poisson distribution models the number of events in a fixed interval given average rate λ. P(X=k) = (e^−λ × λᵏ) / k!. Both the mean and variance equal λ.
分步指南
- 1P(X=k) = (e^−λ × λᵏ) / k!
- 2λ = average number of events per interval
- 3Events must be independent and occur at constant average rate
例题解析
输入
λ=3 calls/min · P(exactly 5 calls)
结果
P = e^−3 × 3⁵/120 ≈ 10.1%
Classic Poisson application
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