Let X1,., X, be a random sample from a uniform distribution on the interval (0, 50], where 0 > 0. Thus, the population pdf is if 0 < r< 50 50 fo(x) = 0, otherwise. (a) Show that the population mean and variance are: E,(X) = (2.5)0 and V,(X) = (登)P. (b) Derive a method of moments estimator of 0 based on X1,..., Xn. (c) Derive the bias and MSE formulas for your method of moments estimator. (d) Give the likelihood function, clearly specifying its argument and domain (input space). Draw a rough sketch of the likelihood function and derive the maximum likelihood estimator of 0, with clear explanation.

Let X1,., X, be a random sample from a uniform distribution on the interval (0, 50], where 0 > 0. Thus, the population pdf is if 0 < r< 50 50 fo(x) = 0, otherwise. (a) Show that the population mean and variance are: E,(X) = (2.5)0 and V,(X) = (登)P. (b) Derive a method of moments estimator of 0 based on X1,..., Xn. (c) Derive the bias and MSE formulas for your method of moments estimator. (d) Give the likelihood function, clearly specifying its argument and domain (input space). Draw a rough sketch of the likelihood function and derive the maximum likelihood estimator of 0, with clear explanation.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.1: Measures Of Center

Problem 9PPS

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