Let Y1, Y2, . . . , Yn denote a random sample from the density function given by
where α > 0 is known.
a Find the MLE of θ.
b Find the expected value and variance of .
c Show that is consistent for θ.
d What is the best (minimal) sufficient statistic for θ in this problem?
e Suppose that n = 5 and α = 2. Use the minimal sufficient statistic to construct a 90% confidence interval for θ. [Hint: Transform to a χ 2 distribution.]
Step 1 of 3
Chapter Notes: Causal Inference ● Ultimate goal of scientific method ● Dependent Variable = Phenomenon we want to explain. (We denote with Y) ● Independent Variable = Variable that we hypothesize causes Dependent Variable to vary. (We denote with X) Fundamental Problem of Causal Inference ● Two States of the World: ○ 1) What we observe happen to Y given X=A ○ 2) Counterfactual: What would have happened to Y had X = B observed No effect Positive effect Negative counterfactual counterfactual effect counterfactual Conservative 90 90 80
Textbook: Mathematical Statistics with Applications
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
This full solution covers the following key subjects: Find, sufficient, Statistic, minimal, known. This expansive textbook survival guide covers 32 chapters, and 3350 solutions. Since the solution to 85E from 9 chapter was answered, more than 327 students have viewed the full step-by-step answer. Mathematical Statistics with Applications was written by and is associated to the ISBN: 9780495110811. The full step-by-step solution to problem: 85E from chapter: 9 was answered by , our top Statistics solution expert on 07/18/17, 08:07AM. The answer to “Let Y1, Y2, . . . , Yn denote a random sample from the density function given by where ? > 0 is known.a Find the MLE of ?.b Find the expected value and variance of .c Show that is consistent for ?.d What is the best (minimal) sufficient statistic for ? in this problem?e Suppose that n = 5 and ? = 2. Use the minimal sufficient statistic to construct a 90% confidence interval for ?. [Hint: Transform to a ? 2 distribution.]” is broken down into a number of easy to follow steps, and 84 words. This textbook survival guide was created for the textbook: Mathematical Statistics with Applications , edition: 7.