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Question: b for n 100 give an approximaation for pygt...

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(b) For n = 100, give an approximaation for P(Y> 100) (c) Let X be the sample mean, then approximate P(1.1< 1.2) for -100. 2. Consider a random sample XX from CDF F(a) 1-1/ for z [1, 0o) and zero otherwise. (a) Find the limiting distribution of XiI.n, the smallest order statistic. (b) Find the limiting distribution of XI (c) Find the limiting distribution of n In X1:m- 3. Suppose that X,,, are iid. N(0,o2). Find a function of T(x)x that con- verges in distribution to a normal distribution. State the mean and variance of your limiting normal distribution. 4. Stirlings Formula, which gives approximation for factorials, can be derived using CLT. (a) Suppose that X,x,.. X is an i.i.d. sample from Exp(1). Show that, for a standard normal random variable Z, X,1-1 (b) Show by differencing both sides of the approximation in part a. Then set x 0 to get Stirlings Formula. 5. Suppose that Y, is an id sample from Negative Binomial (n.p). Give a normal approximation of use CLT, when n is large.
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