a) Let X₁, X₂, ..., Xn denote a random sample from a probability density function given by 1 f(x; a,0) = (T(a)@ª)xª-¹e ,x>0 Where a > 0 is known. x == 0, elsewhere i) Find the maximum likelihood estimator (MLE), say ê of 0. ii) Is the MLE ê a consistent estimator of 0. iii) Use factorisation theorem to find the sufficient statistic for 0?.
a) Let X₁, X₂, ..., Xn denote a random sample from a probability density function given by 1 f(x; a,0) = (T(a)@ª)xª-¹e ,x>0 Where a > 0 is known. x == 0, elsewhere i) Find the maximum likelihood estimator (MLE), say ê of 0. ii) Is the MLE ê a consistent estimator of 0. iii) Use factorisation theorem to find the sufficient statistic for 0?.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 31E
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