/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Q7.1-4E In Example 7.1.6, identify the c... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 7: Q7.1-4E (page 384)

In Example 7.1.6, identify the components of the statistical model as defined in Definition 7.1.1.

Short Answer

Expert verified

The random variables of interest are the observable heights\({X_1}...{X_n}\) the hypothetically observable mean (parameter) \(\mu \) , and the sample mean \({X_n}\). The \({X_i}\) are modelled as normal random variables with mean 渭 and variance 9.

Step by step solution

01

Given information

The heights of men in a certain population follow the normal distribution with mean\(\mu \)and variance 9,

This time, assume that we do not know the value of the mean 渭, but rather we wish to learn about it by sampling from the population. Suppose that we decide to sample

n = 36 men and let \({X_n}\) stand for the average of their heights. Then the interval\(\left( {\overline {{X_n}} - 0.98,\overline {{X_n}} + 0.98} \right)\) computed in Example 5.6.8 has the property that it will contain the value of \(\mu \) with probability 0.95.

02

Defining statistical model.

A statistical model consists of an identification of random variables of interest (both observable and only hypothetically observable),a specification of a joint distribution for the observable random variables, the identification of any parameter of those distribution that are assumed unknown and possibly hypothetically observable, and a specification for a joint distribution for a unknown parameters.

03

Identifying the component of the statistical model

By applying the definition of statistical model to the given information ,The random variables of interest are the observable heights\({X_1}...{X_n}\) the hypothetically observable mean (parameter) \(\mu \) , and the sample mean \({X_n}\). The \({X_i}\) are modelled as normal random variables with mean 渭 and variance 9.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Suppose that a random sample is to be taken from a normal distribution for which the value of the mean 胃 is unknown and the standard deviation is 2, the prior distribution of 胃 is a normal distribution for which the standard deviation is 1, and the value of 胃 must be estimated by using the squared error loss function. What is the smallest random sample that must be taken in order for the mean squared error of the Bayes estimator of 胃 to be 0.01 or less? (See Exercise 10 of Sec. 7.3.)

Consider the data in Example 7.3.10. This time, suppose that we use the improper prior 鈥減.d.f.鈥漒(\xi \left( \theta \right) = 1\)(for all 胃). Find the posterior distribution of\(\theta \)and the posterior probability that\(\theta > 1\).

Question: Suppose that each of two statisticians A and B mustestimate a certain parameter p whose value is unknown(0<p <1). Statistician A can observe the value of a randomvariable X, which has the binomial distribution withparameters n = 10 and p; statistician B can observe thevalue of a random variable Y, which has the negative binomialdistribution with parameters r = 4 and p. Supposethat the value observed by statistician A is X = 4 and thevalue observed by statistician B is Y = 6. Show that thelikelihood functions determined by these observed valuesare proportional, and find the common value of theM.L.E. of p obtained by each statistician.

Show that the family of discrete uniform distributions on the sets of integers \(\left\{ {0,1...\theta } \right\}\) for \(\theta \) a nonnegative integer is not an exponential family as defined in Exercise

Suppose that \({{\bf{X}}_{\bf{1}}}{\bf{,}}...{\bf{,}}{{\bf{X}}_{\bf{n}}}\) form a random sample from the gamma distribution specified in Exercise 6. Show that the statistic \({\bf{T = }}\sum\limits_{{\bf{i = 1}}}^{\bf{n}} {{\bf{log}}{{\bf{x}}_{\bf{i}}}} \) is a sufficient statistic for the parameter\({\bf{\alpha }}\).
See all solutions

Recommended explanations on Math Textbooks

Pure Maths

Read Explanation

Statistics

Read Explanation

Probability and Statistics

Read Explanation

Logic and Functions

Read Explanation

Discrete Mathematics

Read Explanation

Calculus

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.