Let X, X,..., Xn be a random sample of size n from population X. Suppose that...
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Let X₁, X₂,..., Xn be a random sample of size n from population X. Suppose that X has the following probability mass function: x = 1,2,3,... elsewhere f (x; 0) = {0 (1 - 0)×-1, i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = 1 X₁. Hint: Apply f(L(0)|g(8,0)). ii) Based on i) above, is = ₁X₁ a sufficient statistic? Justify your answer. iii) Show whether or not X, is a consistent estimator of the parameter (6) (2) (4) Let X₁, X₂,..., Xn be a random sample of size n from population X. Suppose that X has the following probability mass function: x = 1,2,3,... elsewhere f (x; 0) = {0 (1 - 0)×-1, i) Find the conditional distribution of the likelihood function given the function of the statistic, Ô = 1 X₁. Hint: Apply f(L(0)|g(8,0)). ii) Based on i) above, is = ₁X₁ a sufficient statistic? Justify your answer. iii) Show whether or not X, is a consistent estimator of the parameter (6) (2) (4)
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Mathematical Statistics With Applications In R
ISBN: 9780124171138
2nd Edition
Authors: Chris P. Tsokos, K.M. Ramachandran
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