2. Suppose that a random variable Z has an unknown distribution with a mean of u...
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2. Suppose that a random variable Z has an unknown distribution with a mean of u and a variance of o. We take a sample of n i.i.d observations (2, 22,..., 22), calculate Zn-2 (the sample mean based on the first n-2 observations) and then construct defined by = (Zn-2) + (n-1 + n). a) Show that is an unbiased estimator of and then provide an intuitive explana- tion of why is not consistent for u. b) Find Var(), compare it with Var(Zn-2), and then discuss the efficiency of . Does attain the Cramer Rao lower bound? Briefly explain. Now let Z, Z2,... be a sequence of random variables, and suppose that for n = 1, 2, the probability distribution of Zn is given by Zn 0 n +5 Pr(Zn = Zn) 1 T c) Find an expression for E(Zn) and then briefly discuss why lim E(Zn) does not n-x exist. d) Briefly discuss why plim Zn =0. An intuitive argument is acceptable here. 2. Suppose that a random variable Z has an unknown distribution with a mean of u and a variance of o. We take a sample of n i.i.d observations (2, 22,..., 22), calculate Zn-2 (the sample mean based on the first n-2 observations) and then construct defined by = (Zn-2) + (n-1 + n). a) Show that is an unbiased estimator of and then provide an intuitive explana- tion of why is not consistent for u. b) Find Var(), compare it with Var(Zn-2), and then discuss the efficiency of . Does attain the Cramer Rao lower bound? Briefly explain. Now let Z, Z2,... be a sequence of random variables, and suppose that for n = 1, 2, the probability distribution of Zn is given by Zn 0 n +5 Pr(Zn = Zn) 1 T c) Find an expression for E(Zn) and then briefly discuss why lim E(Zn) does not n-x exist. d) Briefly discuss why plim Zn =0. An intuitive argument is acceptable here.
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a To show that is an unbiased estimator of we need to demonstrate that the expected value of equals the true population mean Lets calculate the expect... View the full answer
Related Book For
Discrete and Combinatorial Mathematics An Applied Introduction
ISBN: 978-0201726343
5th edition
Authors: Ralph P. Grimaldi
Posted Date:
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