question archive In the course, we described how the Poisson(λ) distribution can be derived as the limit of a Binomial(n, p = λ n ) distribution, as n → ∞
In the course, we described how the Poisson(λ) distribution can be derived as the limit of a Binomial(n, p = λ n ) distribution, as n → ∞
Subject:StatisticsPrice: Bought3
In the course, we described how the Poisson(λ) distribution can be derived as the limit of a Binomial(n, p = λ n ) distribution, as n → ∞. For this question, you have to prove this result using MGFs: First, write down the general form of the MGF for the Binomial & Poisson distributions (which can be found here), and then show that the MGF of the Binomial where p = λ n converges to that of the Poisson(λ), as n → ∞ (implying convergence in distribution).
