Math

StatisticsProbability and Statistics for Engineering and the Sciencesa. Let X 1 have a chi-squared distribution with parameter v 1 (see Section 4.4), and let X 2 be independent of X 1 and have a chi-squared distribution with parameter v 2 . Use the technique of Example 5.22 to show that X 1 + X 2 has a chi-squared distribution with parameter v 1 + v 2 . b. In Exercise 71 of Chapter 4, you were asked to show that if Z is a standard normal rv, then Z 2 has a chi-squared distribution with v = 1. Let Z 1 , Z 2 , . . . , Zn be n independent standard normal rv’s. What is the distribution of Z 1 2 +…+ Zn 2 ? Justify your answer. c. Let X 1 , … , X n be a random sample from a normal distribution with mean µ and variance σ 2 . What is the distribution of the sum Y = ∑ i = 1 n [ ( X i − μ ) / σ ] 2 ? Justify your answer.BuyFind*arrow_forward*

9th Edition

Jay L. Devore

Publisher: Cengage Learning

ISBN: 9781305251809

Chapter 5, Problem 91SE

Textbook Problem

**a.** Let *X*_{1} have a chi-squared distribution with parameter *v*_{1} (see Section 4.4), and let *X*_{2} be independent of *X*_{1} and have a chi-squared distribution with parameter *v*_{2}. Use the technique of Example 5.22 to show that *X*_{1} + *X*_{2} has a chi-squared distribution with parameter *v*_{1} + *v*_{2}.

**b.** In Exercise 71 of Chapter 4, you were asked to show that if *Z* is a standard normal rv, then *Z*^{2} has a chi-squared distribution with *v* = 1. Let *Z*_{1}, *Z*_{2}, . . . , *Zn * be *n* independent standard normal rv’s. What is the distribution of *Z*_{1}^{2} +…+ *Zn ^{2}* ? Justify your answer.

**c.** Let *X*_{1}, … , *X _{n}* be a random sample from a normal distribution with mean

Probability and Statistics for Engineering and the Sciences

Show all chapter solutions

Ch. 5.1 - A service station has both self-service and...Ch. 5.1 - A large but sparsely populated county has two...Ch. 5.1 - A certain market has both an express checkout line...Ch. 5.1 - Return to the situation described in Exercise 3....Ch. 5.1 - The number of customers waiting for gift-wrap...Ch. 5.1 - Let X denote the number of Canon SLR cameras sold...Ch. 5.1 - The joint probability distribution of the number X...Ch. 5.1 - A stockroom currently has 30 components of a...Ch. 5.1 - Each front tire on a particular type of vehicle is...Ch. 5.1 - Annie and Alvie have agreed to meet between 5:00...

Ch. 5.1 - Two different professors have just submitted final...Ch. 5.1 - Two components of a minicomputer have the...Ch. 5.1 - You have two lightbulbs for a particular lamp. Let...Ch. 5.1 - Suppose that you have ten lightbulbs, that the...Ch. 5.1 - Consider a system consisting of three components...Ch. 5.1 - a. For f(x1, x2, x3) as given in Example 5.10,...Ch. 5.1 - An ecologist wishes to select a point inside a...Ch. 5.1 - Refer to Exercise 1 and answer the following...Ch. 5.1 - The joint pdf of pressures for right and left...Ch. 5.1 - Let X1, X2, X3, X4, X5, and X6 denote the numbers...Ch. 5.1 - Let X1, X2, and X3 be the lifetimes of components...Ch. 5.2 - An instructor has given a short quiz consisting of...Ch. 5.2 - The difference between the number of customers in...Ch. 5.2 - Six individuals, including A and B, take seats...Ch. 5.2 - A surveyor wishes to lay out a square region with...Ch. 5.2 - Consider a small ferry that can accommodate cars...Ch. 5.2 - Annie and Alvie have agreed to meet for lunch...Ch. 5.2 - Show that if X and Y are independent rvs, then...Ch. 5.2 - Compute the correlation coefficient for X and Y...Ch. 5.2 - a. Compute the covariance for X and Y in Exercise...Ch. 5.2 - a. Compute the covariance between X and Y in...Ch. 5.2 - Reconsider the minicomputer component lifetimes X...Ch. 5.2 - Use the result of Exercise 28 to show that when X...Ch. 5.2 - a. Recalling the definition of 2 for a single rv...Ch. 5.2 - a. Use the rules of expected value to show that...Ch. 5.2 - Show that if Y = aX + b (a 0), then Corr(X, Y)...Ch. 5.3 - A particular brand of dishwasher soap is sold in...Ch. 5.3 - There are two traffic lights on a commuters route...Ch. 5.3 - It is known that 80% of all brand A external hard...Ch. 5.3 - A box contains ten sealed envelopes numbered 1, ....Ch. 5.3 - Let X be the number of packages being mailed by a...Ch. 5.3 - A company maintains three offices in a certain...Ch. 5.3 - Suppose the amount of liquid dispensed by a...Ch. 5.4 - Youngs modulus is a quantitative measure of...Ch. 5.4 - Refer to Exercise 46. Suppose the distribution is...Ch. 5.4 - The National Health Statistics Reports dated Oct....Ch. 5.4 - There are 40 students in an elementary statistics...Ch. 5.4 - Let X denote the courtship time for a randomly...Ch. 5.4 - The time taken by a randomly selected applicant...Ch. 5.4 - The lifetime of a certain type of battery is...Ch. 5.4 - Rockwell hardness of pins of a certain type is...Ch. 5.4 - Suppose the sediment density (g/cm) of a randomly...Ch. 5.4 - The number of parking tickets issued in a certain...Ch. 5.4 - A binary communication channel transmits a...Ch. 5.4 - Suppose the distribution of the time X (in hours)...Ch. 5.5 - A shipping company handles containers in three...Ch. 5.5 - Let X1, X2, and X3 represent the times necessary...Ch. 5.5 - Refer back to Example 5.31. Two cars with...Ch. 5.5 - Exercise 26 introduced random variables X and Y,...Ch. 5.5 - Manufacture of a certain component requires three...Ch. 5.5 - Refer to Exercise 3. a. Calculate the covariance...Ch. 5.5 - Suppose your waiting time for a bus in the morning...Ch. 5.5 - Suppose that when the pH of a certain chemical...Ch. 5.5 - If two loads are applied to a cantilever beam as...Ch. 5.5 - One piece of PVC pipe is to be inserted inside...Ch. 5.5 - Two airplanes are flying in the same direction in...Ch. 5.5 - Three different roads feed into a particular...Ch. 5.5 - Consider a random sample of size n from a...Ch. 5.5 - In Exercise 66, the weight of the beam itself...Ch. 5.5 - I have three errands to take care of in the...Ch. 5.5 - Suppose the expected tensile strength of type-A...Ch. 5.5 - In an area having sandy soil, 50 small trees of a...Ch. 5 - A restaurant serves three fixed-price dinners...Ch. 5 - In cost estimation, the total cost of a project is...Ch. 5 - A health-food store stocks two different brands of...Ch. 5 - According to the article Reliability Evaluation of...Ch. 5 - Suppose that for a certain individual, calorie...Ch. 5 - The mean weight of luggage checked by a randomly...Ch. 5 - We have seen that if E(X1) = E(X2) = =E(Xn) = ,...Ch. 5 - Suppose the proportion of rural voters in a...Ch. 5 - Let denote the true pH of a chemical compound. A...Ch. 5 - If the amount of soft drink that I consume on any...Ch. 5 - Refer to Exercise 58, and suppose that the Xis are...Ch. 5 - A student has a class that is supposed to end at...Ch. 5 - Garbage trucks entering a particular...Ch. 5 - Each customer making a particular Internet...Ch. 5 - a. Use the general formula for the variance of a...Ch. 5 - Suppose a randomly chosen individuals verbal score...Ch. 5 - a. Let X1 have a chi-squared distribution with...Ch. 5 - a. Show that Cov(X, Y + Z) = Cov(X, Y) + Cov(X,...Ch. 5 - A rock specimen from a particular area is randomly...Ch. 5 - Let A denote the percentage of one constituent in...Ch. 5 - Let X1, . . . , Xn be independent rvs with mean...Ch. 5 - A more accurate approximation to E[h(X1, . . . ,...Ch. 5 - Let X and Y be independent standard normal random...Ch. 5 - Let X1, X2, . . . , Xn be random variables...

Find more solutions based on key concepts

Show solutions Are the following workers more likely to experience short-term or long-term unemployment? Explain. a. a constru...

Principles of Macroeconomics (MindTap Course List)

You win 100 in a basketball pool. You have a choice between spending the money now and putting it away for a ye...

Principles of Economics (MindTap Course List)

A manager of a large corporation recommends a 10,000 raise be given to keep a valued subordinate from moving to...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Approximately how long does it take a change in monetary policy to influence aggregate demand? a. 1 month b. 6 ...

Brief Principles of Macroeconomics (MindTap Course List)

(Barriers to Entry) Identify the other two barriers to entry and explain how they block new firms from this mar...

ECON: MICRO4 (New, Engaging Titles from 4LTR Press)

Classify the following topics as relating to microeconomics or macroeconomics. a. a familys decision about how ...

Principles of Microeconomics (MindTap Course List)

Because there are computer-based documentation products that can draw data flow diagrams and systems flowcharts...

Accounting Information Systems

Exercise Issuance and Interest Amortization for Zero Coupon Note (Straight Line) Kerwin Company borrowed $10,00...

Cornerstones of Financial Accounting

How can the Federal Reserve and government use monetary policy and fiscal policy to reduce the effects of an ec...

Foundations of Business (MindTap Course List)

EXPECTED INTEREST RATE Lourdes Corporations 12% coupon rate, semiannual payment, 1,000 par value bonds, which m...

Fundamentals Of Financial Management, Concise Edition (mindtap Course List)

If inventory is being valued at cost and the price level is steadily rising, which of the three methods of cost...

Financial & Managerial Accounting

Entries for note collected by bank Accompanying a bank statement for Borden Company is a credit memo for 21,200...

Corporate Financial Accounting

BETA AND REQUIRED RATE OF RETURN A stock has a required return of 9%, the risk-free rate is 4.5%, and the marke...

Fundamentals of Financial Management (MindTap Course List)

Great news! GeekTech, the start-up company where you work, has become enormously successful. Now the owner want...

Essentials of Business Communication (MindTap Course List)

Differentiate between dealer markets and stock markets that have a physical location.

Fundamentals of Financial Management, Concise Edition (MindTap Course List)

SOC Labor force participation rates percent employed, percent high school graduates, and mean income for males ...

Essentials Of Statistics

Ackerman and Goldsmith (2011) found that students who studied text from printed hardcopy had letter test scores...

Statistics for The Behavioral Sciences (MindTap Course List)

Draw a histogram for the distribution of scores shown in the following table. x f 10 2 9 4 8 1 7 1 6 4 5 2

Essentials of Statistics for The Behavioral Sciences (MindTap Course List)

Basic Computation: Weighted Average Find the weighted average of a data set where 10 has a weight of 2; 20 has ...

Understanding Basic Statistics

At what points does the curve r(t) = t i + (2t t2) k intersect the paraboloid z = x2 + y2?

Multivariable Calculus

Sketching the Graph of an Equation in Exercises 7-22, sketch the graph of the equation. Use a graphing utility ...

Calculus: An Applied Approach (MindTap Course List)

Prove that dndxn(sin4x+cos4x)=4n1cos(4x+n/2).

Calculus: Early Transcendentals

Finding the Center of Mass Using Technology In Exercises 25-28, use a computer algebra system to find the mass ...

Calculus: Early Transcendental Functions

Simplify each expression in Exercises 1730, expressing your answer in positive exponent form. (xy2zx1z)3

Applied Calculus

Find the functions (a) f g, (b) g f, (c) f f, and (d) g g and their domains. 38. f(x)=x1+x, g(x) = sin 2x

Single Variable Calculus: Early Transcendentals, Volume I

In Exercises 2934, rationalize the denominator of each expression. 33. a+bab

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Polar Form of Complex Numbers Write the complex number in polar form with argument between 0 and 2. 43. 4 + 3i

Precalculus: Mathematics for Calculus (Standalone Book)

Convert each expression in Exercises 25-50 into its technology formula equivalent as in the table in the text. ...

Finite Mathematics and Applied Calculus (MindTap Course List)

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or gi...

Single Variable Calculus

Evaluate the surface integral. sFdS, where F(x,y,z)=x2i+xyj+zk and S is the part of the paraboloid z=x2+y2 belo...

Calculus (MindTap Course List)

Convert the expressions in Exercises 6584 to power form. xy23

Finite Mathematics

For Problems 56-64, use your calculator to evaluate each numerical expression. Objective 3 37

Intermediate Algebra

Solve each of the following triangles. a=76.3m,c=42.8m,B=16.3

Trigonometry (MindTap Course List)

Which numbers are divisible a. by 3 and b. by 4? 96

Elementary Technical Mathematics

29. Politics A political candidate wants to use a combination of radio and TV advertisements in her campaign. R...

Mathematical Applications for the Management, Life, and Social Sciences

Determine the nth-term formula for the number of square tiles in the nth figure.

Mathematical Excursions (MindTap Course List)

In Exercises 19 to 24, complete each proof. Given: 12and34 Prove: MNPQ is a kite PROOF Statements Reasons 1. 1...

Elementary Geometry For College Students, 7e

For the following investments, find the total number of compounding periods and the interest rate per period.
T...

Contemporary Mathematics for Business & Consumers

1. For the given sets, form the Cartesian product.

Elements Of Modern Algebra

Finding a Power Series In Exercises 7-18, find a power series for the function, centered at c, and determine th...

Calculus of a Single Variable

The payoff matrix for a game is given by [1223] Compute the expected payoffs of the game for the pairs of strat...

Finite Mathematics for the Managerial, Life, and Social Sciences

Consider the tangent line to the ellipse x2a2+y2b2=1 at a point (p, q) in the first quadrant. (a) Show that the...

Single Variable Calculus: Early Transcendentals

Finding Points of Inflection In Exercises 1334, find the points of inflection and discuss the concavity of the ...

Calculus: Early Transcendental Functions (MindTap Course List)

The accompanying data on number of minutes used for cell phone calls in 1 month was generated to be consistent ...

Introduction To Statistics And Data Analysis

Let F(x, y, z) = Pi + Qj + Rk have continuous first partial derivatives and E be a simple solid with boundary s...

Study Guide for Stewart's Multivariable Calculus, 8th

Given that point P does not lie on the line l, construct the line through point P that is parallel to line l.

Elementary Geometry for College Students

Estimate 14(x3x2) using the Left Endpoint Rule and n = 5. a) 203 b) 20 c) 24 d) 30

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

Define the two general categories of statistics, descriptive and inferential, and explain the purpose for each.

Research Methods for the Behavioral Sciences (MindTap Course List)

An acceptance sampling plan with n = 15 and c = 1 has been designed with a producers risk of .075. a. Was the v...

Statistics for Business & Economics, Revised (MindTap Course List)

Describe how the cliche You can lead a horse to water, but you cant make it drink can be used to explain a pers...

Research Methods for the Behavioral Sciences (MindTap Course List)

Projectile MotionIn Exercises 41 and 42, use the model for projectile motion, assuming there is no air resistan...

Multivariable Calculus

Write each system as a matrix and solve it by Gaussian-Jordan elimination. If a system has infinitely many solu...

College Algebra (MindTap Course List)

Finding intervals of Convergence In Exercises 49-52, find the intervals of convergence of (a) f(x), (b) f(x). (...

Calculus (MindTap Course List)

Express each value as a percent. 18. 0.0639

Mathematics For Machine Technology

Aerospace Part Manufacturing. The competitive advantage of small American factories such as Tolerance Contract ...

Essentials Of Statistics For Business & Economics

46. Phone calls arrive at the rate of 48 per hour at the reservation desk for Regional Airways.
Compute the pro...

Modern Business Statistics with Microsoft Office Excel (with XLSTAT Education Edition Printed Access Card) (MindTap Course List)

Determine the validity of the arguments in Exercises 67 and 68 by constructing a a. Venn diagram and a b. truth...

Mathematics: A Practical Odyssey

Find the first four terms every of the recursively defined sequences in 1-8. ak=2ak1+k , for every integer k2 a...

Discrete Mathematics With Applications

Each DE in Problems 114 is homogeneous. In Problems 110 solve the given differential equation by using an appro...

A First Course in Differential Equations with Modeling Applications (MindTap Course List)

Reminder Round all answers to two decimal places unless otherwise indicated. Speed and Stride Length The speed ...

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

Use the following information to answer the next twelve exercises. In the recent Census, three percent of the U...

Introductory Statistics

For the following exercises, find the domain, range, and all zeros/intercepts, if any, of the functions. 14. f(...

Calculus Volume 1