2018 November 10,

Math 265: Day 26

Carleton College, Joshua R. Davis

A. Section 10.7 Exercise 21.

B. Using the CLT, explain why X ~ Pois(n) is approximately normal when n is a large positive integer. And find the parameters of that normal distribution.

C. Let Y ~ Norm(μ, σ²). Explain why P(μ - 1 / 2 < Y < μ + 1 / 2) is approximately (2 π σ²)^{-1 / 2} when σ² is large.

D. Using Problems B and C above, explain Stirling's approximation to the factorial: When n is large, n! is approximately (2 π n)^{1 / 2} (n / e)ⁿ.