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The Poisson distribution

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Useful for: IB Math AI HL

Learn it For events happening at an average rate λ in a fixed interval (calls per hour, typos per page): P(X = k) = e⁻λ λᵏ/k!. Mean and variance both equal λ. Rates scale: 3 per hour means 6 per two hours.

Example: A help desk gets 4 calls an hour on average. P(exactly 2 in an hour)?

  1. e⁻⁴ × 4²/2!
  2. ≈ 0.147.

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