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3. Suppose that X1,X2, ,Xn are i.id. N(0, σ2). Find a function of T(X)-Σǐii verges in distribution to a normal distribution. State the mean and variance of your limiung normal distribution. 4. Stirlings Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X1, X2, random variable Z, .Xn is an ii.d. sample from Exp(1). Show that, for a standard normal PTPZ) (b) Show by differencing both sides of the approximation in part a. Then set z= 0 to get Stirlings Formula. 5. Suppose that Yn is an iid sample from Negative Binomial (n.p). Give a normal approximation of 曲頎啅 0%回 DOLL Type here to search
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