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Exercise 4.18 Suppose that X1, X2, ... are independent binomial(2, p) random vari- ables. Define Y = NX; = 0}. (a) Find a such that

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Exercise 4.18 Suppose that X1, X2, ... are independent binomial(2, p) random vari- ables. Define Y = NX; = 0}. (a) Find a such that the joint asymptotic distribution of In a is nontrivial, and find this joint asymptotic distribution. (b) Using the Cramer-Wold Theorem, Theorem 4.12, find the asymptotic dis- tribution of vn(X, + Yn -1 -p')

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