Subject:  Statistics

Poisson probability: P(X = 2) with λ = 3

Compute a Poisson point probability and its cumulative tails.

Answer P(X = 2) = 0.224042, P(X ≤ 2) = 0.42319, P(X ≥ 2) = 0.800852

Solution

  1. Distribution X ~ Poisson(λ = 3)
  2. P(X = k) e^(−λ)·λ^k/k! = e^(−3)·3^2/2! = 0.224042
  3. P(X ≤ k) 0.42319
  4. P(X < k) 0.199148
  5. P(X ≥ k) 1 − P(X < k) = 0.800852
  6. Mean μ = λ = 3
  7. Variance σ² = λ = 3
  8. Standard deviation σ = √λ = 1.73205

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