By considering the Poisson distribution, show that \[ e^{-n}\left (1+n+\frac {n^2}{2!}+\cdots +\frac {n^n}{n!}\right )\to \frac {1}{2} \] as \(n\to \infty \).
Question
Math 6010 • Linear Models
Fall 2010 • Question 10
Question
Fall 2010 • Question 10
By considering the Poisson distribution, show that \[ e^{-n}\left (1+n+\frac {n^2}{2!}+\cdots +\frac {n^n}{n!}\right )\to \frac {1}{2} \] as \(n\to \infty \).