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3. stirlings formula which gives approximation for factorials can be derived...

# 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.