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CSS Statistics QUESTION #1980
Question 1
The Poisson distribution is derived as the limiting form of the Binomial distribution when:
  • n is small and p is large
  • n is large, p is small, and \(np = \lambda\) remains constant✔️
  • n and p both approach zero
  • n is fixed and p approaches 0.5
Correct Answer Explanation
The Poisson distribution arises as \(n \to \infty\) and \(p \to 0\) such that \(\lambda = np\) remains a finite constant. Under these conditions, \(\binom{n}{x}p^x(1-p)^{n-x} \to \dfrac{e^{-\lambda}\lambda^x}{x!}\).