Poisson distribution models rare events in fixed interval. P(X=k) = (e^(-λ) × λ^k) / k!. Mean = Variance = λ (key property). Example: Accidents/month, λ=3. P(X=2) = (e^(-3) × 3²) / 2! = (0.0498 × 9) / 2 ≈ 0.2240. Assumptions: Events independent, constant rate, no clustering. When to use: Rare events, interval data (time, distance, area). Compared to binomial: Poisson for large n, small p, np=λ. Normal approximation: When λ > 5. Solving: Identify λ. Use formula or Poisson tables. Exam tip: Recognize Poisson applications. Use normal approximation for large λ. Practice: Defects, arrivals, occurrences problems.