Question: stirlings formula which gives approximation for factorials can be derived...
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,
by differencing both sides of the approximation in part a. Then set x = 0 to get Stirling’s Formula.