# Question: stirlings formula which gives approximation for factorials can be derived...

###### Question details

Stirling’s Formula, which gives approximation for factorials,
can be derived using CLT.

(a) Suppose that X1, X2, · · · , Xn is an i.i.d. sample from
Exp(1). Show that, for a standard normal

random variable Z,

(b) Show

by differencing both sides of the approximation in part a. Then set x = 0 to get Stirling’s Formula.