Poisson probability: P(X = 2) with λ = 3
Compute a Poisson point probability and its cumulative tails.
Solution
- Distribution X ~ Poisson(λ = 3)
- P(X = k) e^(−λ)·λ^k/k! = e^(−3)·3^2/2! = 0.224042
- P(X ≤ k) 0.42319
- P(X < k) 0.199148
- P(X ≥ k) 1 − P(X < k) = 0.800852
- Mean μ = λ = 3
- Variance σ² = λ = 3
- Standard deviation σ = √λ = 1.73205
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