Poisson: Customer Arrivals

Probability · Axiom Academy

EXAMPLE Poisson Distribution: Customer Arrivals Customers arrive at a store at an average rate of 4 per hour. Find P(exactly 3 arrive in next hour) and P(at least 2 arrive). Excellent work! You've completed this Poisson distribution example. Here's what we learned: Poisson distribution: Models the number of events occurring in a fixed interval of time or space when events occur at a constant average rate λ. Poisson formula: P(X = k) = (λ^k × e^(-λ)) / k! where λ is the average rate and k is the number of events. Complement rule: For "at least" problems, it's often easier to calculate P(X ≥ k) = 1 - P(X < k) rather than summing many terms. Special value: e^(-4) ≈ 0.0183 is used throughout Poisson calculations with λ = 4. The Poisson distribution is perfect for rare events over time, like customer arrivals, phone calls, or radioactive decay. Practice with different rates!

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