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24. Let X1,,Xn be a sample from a population with mean and variance 2<. Suppose h has a second derivative h(2) continuous at and that h(1)()=0. (a) Show that n[h(X)h()]0 while n[h(Xh()] is asymptotically distributed as 21h(2)()2V where V12. (b) Use part (a) to show that when =21,n[X(1 X)(1)]S2V with V12. Give an approximation to the distribution of X(1X) in terms of the 12 distribution function when =21..

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24. Let X1,,Xn be a sample from a population with mean and variance 2<. Suppose h has a second derivative h(2) continuous at and that h(1)()=0. (a) Show that n[h(X)h()]0 while n[h(Xh()] is asymptotically distributed as 21h(2)()2V where V12. (b) Use part (a) to show that when =21,n[X(1 X)(1)]S2V with V12. Give an approximation to the distribution of X(1X) in terms of the 12 distribution function when =21.

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24 Let X1Xn be a sample from a population with mean and.pdf

  • 1. 24. Let X1,,Xn be a sample from a population with mean and variance 2<. Suppose h has a second derivative h(2) continuous at and that h(1)()=0. (a) Show that n[h(X)h()]0 while n[h(Xh()] is asymptotically distributed as 21h(2)()2V where V12. (b) Use part (a) to show that when =21,n[X(1 X)(1)]S2V with V12. Give an approximation to the distribution of X(1X) in terms of the 12 distribution function when =21.