Find the probability limits (if they exist) of the following sequences of random variables (a) Zn U 0,1 n (b) Zn Bernoulli(pn) with pn 11 n (c) Zn Poisson(n) with n 1 n (d) Zn exponential(n) with n 1 n (e) Zn Pareto(n,) with 1 and n n (f ) Zn gamma(n,n) with n n and n n (g) Zn Xn n with Xn binomial...

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Find the probability limits (if they exist) of the following sequences of random variables (a) Zn U[0,1/n].

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Find the probability limits (if they exist) of the following sequences of random variables

(a) Zn »U[0,1/n].

(b) Zn »Bernoulli(pn) with pn Æ 1¡1/n.

(c) Zn »Poisson(¸n) with ¸n Æ 1/n.

(d) Zn »exponential(¸n) with ¸n Æ 1/n.

(e) Zn »Pareto(®n,¯) with ¯ Æ 1 and ®n Æ n.

(f ) Zn »gamma(®n,¯n) with ®n Æ n and ¯n Æ n.

(g) Zn Æ Xn/n with Xn »binomial(n,p).

(h) Zn has mean ¹ and variance a/nr for a È 0 and r È 0.

(i) Zn Æ X(n), the nth order statistic when X »U[0,1].

(j) Zn Æ Xn/n where Xn » Â2 n.

(k) Zn Æ 1/Xn where Xn » Â2 n.

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Probability And Statistics For Economists

ISBN: 9780691235943

1st Edition

Authors: Bruce Hansen

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Question Posted: Sep 23, 2024 07:00 AM

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Find the probability limits (if they exist) of the following sequences of random variables (a) Zn U[0,1/n].

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Probability And Statistics For Economists

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