Solution Found!

Statistics / Probability and Statistical Inference 9 / Chapter 2.2 / Problem 8E

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Change Question

Let X be a random variable with support {1, 2, 3, 5, 15,

Chapter 2, Problem 8E

(choose chapter or problem)

Get Unlimited Answers

QUESTION:

Problem 8E

Let X be a random variable with support {1, 2, 3, 5, 15, 25, 50}, each point of which has the same probability 1/7. Argue that c = 5 is the value that minimizes h(c) = E( |X − c| ). Compare c with the value of b that minimizes g(b) = E[(X − b)2].

Questions & Answers

QUESTION:

Problem 8E

Let X be a random variable with support {1, 2, 3, 5, 15, 25, 50}, each point of which has the same probability 1/7. Argue that c = 5 is the value that minimizes h(c) = E( |X − c| ). Compare c with the value of b that minimizes g(b) = E[(X − b)2].

ANSWER:

Solution 8E

Step1 of 2:

We have A random variable X with support {1, 2, 3, 5, 15, 25, 50},each point of which has the same probability 1/7.

We need to Argue that c = 5 is the value that minimizes h(c) = E( |X − c| ). Compare c with the value of b that minimizes g(b) = E[(X − b)2].

Step2 of 2:

Consider a function $h(c)=E(\left|{X-c}\right|)$

= $\sum\limits_{i=1}^{7}{p}_{i}(\left|{{X}_{i}-c}\right|)$

= $\frac{1}{7}\sum\limits_{i}^{\ }$ $\left|{{X}_{i}-c}\right|$

$\leq{}\ \frac$

Study Tools You Might Need

Chapter: 2 Problem: 85E

Mathematical Statistics with Applications 7
If and are independent events, show that and \(\bar{B}\) are also independent. Are \(\bar{A}\) and \(\bar{B}\) independent? Equation Transcription: Text Transcription: B bar A bar B bar

Chapter: 3 Problem: 27P

Chemistry 11
Calculate the number of C, H, and O atoms in 1.50 g of glucose \(\left(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}\right)\), a sugar.

Chapter: 4 Problem: 20

Anatomy & Physiology 1
In adults, new connective tissue cells originate from the ________. a. mesoderm b. mesenchyme c. ectoderm d. endoderm

Chapter: 21 Problem: 2

Glencoe Accounting: First Year Course, Student Edition 1
Distributing Corporate Earnings During its first year of operation, Longhorn Corporation issued 17,500 shares of $10 par common stock. At the end of the year, the corporation had a net income of $350,000. The board of directors declared a cash dividend of $5 per share. Instructions Answer these q

Chapter: 2 Problem: 52

Differential Equations with Boundary-Value Problems 9
Reread the discussion following Example 5. Construct a linear first-order differential equation for which all solutions are asymptotic to the line y = 3x - 5 as \(x \rightarrow \infty\)

Chapter: 9 Problem: 123

Plant Systematics 3
What is the difference between alternate and distichous? Between opposite and decussate?

Chapter: 27 Problem: 8

Principles of Economics 9
According to the efficient markets hypothesis, a. excessive diversification can reduce an investors expected portfolio returns. b. changes in stock prices are impossible to predict from public information. c. actively managed mutual funds should generate higher returns than index funds. d. the stock

Chapter: 4 Problem: 90

College Physics: Explore and Apply 2
The mass of a spacecraft is about 480 kg. An engine designed to increase the speed of the spacecraft while in outer space provides 0.09-N thrust at maximum power. By how much does the engine cause the crafts speed to change in 1 week of running at maximum power? Describe any assumptions you made.

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

×

Register

Sign up for access to all content on our site!

Or login if you already have an account