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Is the estimator consistent? Is the estimator unbiased?

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

Let X be a binomial random variable with parameters n = 20 and p

If you take a sample from a binomial population with known p and unknown n, find the maximum likelihood estimator. (Let N = sample size.)

Is the estimator consistent?

Is the estimator unbiased?

What is the distribution and parameters of the estimator if the sample size N is large?

Find the probability the estimator is incorrect by more than 0.2 if N = 50.

Definition Definition Number of subjects or observations included in a study. A large sample size typically provides more reliable results and better representation of the population. As sample size and width of confidence interval are inversely related, if the sample size is increased, the width of the confidence interval decreases.

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