An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 4.3, Problem 12Q
To determine
Whetherit can be argued that hypnosis does have an effect on a person’s ESP ability.
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A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected.
a) Calculate the percentage of components that get rejected.
b) In a manufacturing run of 1000 units, how many are expected to be rejected?
c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.
5. Let X and Y be independent random variables and let the superscripts denote
symmetrization (recall Sect. 3.6). Show that
(X + Y) X+ys.
8. Suppose that the moments of the random variable X are constant, that is, suppose
that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.
Chapter 4 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 4.2 - If a typist averages one misspelling in every 3250...Ch. 4.2 - A medical study recently documented that 905...Ch. 4.2 - Five hundred people are attending the first annual...Ch. 4.2 - A chromosome mutation linked with colorblindness...Ch. 4.2 - Suppose that 1% of all items in a supermarket are...Ch. 4.2 - A newly formed life insurance company has...Ch. 4.2 - According to an airline industry report (189),...Ch. 4.2 - Electromagnetic fields generated by power...Ch. 4.2 - Astronomers estimate that as many as one hundred...Ch. 4.2 - During the latter part of the nineteenth century,...
Ch. 4.2 - A random sample of three hundred fifty-six seniors...Ch. 4.2 - Midwestern Skies books ten commuter flights each...Ch. 4.2 - Prob. 13QCh. 4.2 - Prob. 14QCh. 4.2 - Prob. 15QCh. 4.2 - A tool and die press that stamps out cams used in...Ch. 4.2 - In a new fiber-optic communication system,...Ch. 4.2 - Assume that the number of hits, X, that a...Ch. 4.2 - Prob. 19QCh. 4.2 - Suppose a radioactive source is metered for two...Ch. 4.2 - Suppose that on-the-job injuries in a textile mill...Ch. 4.2 - Find P(X=4) if the random variable X has a Poisson...Ch. 4.2 - Prob. 23QCh. 4.2 - Prob. 24QCh. 4.2 - Prob. 25QCh. 4.2 - Prob. 26QCh. 4.2 - Records show that deaths occur at the rate of 0.1...Ch. 4.2 - Fifty spotlights have just been installed in an...Ch. 4.2 - Prob. 29QCh. 4.3 - Use Appendix Table A.1 to evaluate the following...Ch. 4.3 - Let Z be a standard normal random variable. Use...Ch. 4.3 - (a) Let 0ab. Which number is larger?...Ch. 4.3 - Prob. 4QCh. 4.3 - Assume that the random variable Z is described by...Ch. 4.3 - Prob. 6QCh. 4.3 - Prob. 7QCh. 4.3 - Hertz Brothers, a small, family-owned radio...Ch. 4.3 - Prob. 9QCh. 4.3 - State Techs basketball team, the Fighting...Ch. 4.3 - A random sample of 747 obituaries published...Ch. 4.3 - Prob. 12QCh. 4.3 - If pX(k)=(10k)(0.7)k(0.3)10k,k=0,1,10, is it...Ch. 4.3 - A sell-out crowd of 42,200 is expected at...Ch. 4.3 - A fair coin is tossed two hundred times. Let Xi=1...Ch. 4.3 - Suppose that one hundred fair dice are tossed....Ch. 4.3 - Let X be the amount won or lost in betting $5 on...Ch. 4.3 - Prob. 18QCh. 4.3 - An electronics firm receives, on the average,...Ch. 4.3 - Prob. 20QCh. 4.3 - Econo-Tire is planning an advertising campaign for...Ch. 4.3 - A large computer chip manufacturing plant under...Ch. 4.3 - Prob. 23QCh. 4.3 - Prob. 24QCh. 4.3 - A criminologist has developed a questionnaire for...Ch. 4.3 - The cross-sectional area of plastic tubing for use...Ch. 4.3 - At State University, the average score of the...Ch. 4.3 - A college professor teaches Chemistry 101 each...Ch. 4.3 - Suppose the random variable Y can be described by...Ch. 4.3 - It is estimated that 80% of all eighteen-year-old...Ch. 4.3 - Prob. 31QCh. 4.3 - Prob. 32QCh. 4.3 - The IQs of nine randomly selected people are...Ch. 4.3 - Let Y1,Y2,...,Yn be a random sample from a normal...Ch. 4.3 - A circuit contains three resistors wired in...Ch. 4.3 - Prob. 36QCh. 4.3 - Use moment-generating functions to prove the two...Ch. 4.3 - Let Y1,Y2,...,Y9 be a random sample of size 9 from...Ch. 4.3 - Prob. 39QCh. 4.4 - Because of her past convictions for mail fraud and...Ch. 4.4 - A teenager is trying to get a drivers license....Ch. 4.4 - Prob. 3QCh. 4.4 - Recently married, a young couple plans to continue...Ch. 4.4 - Show that the cdf for a geometric random variable...Ch. 4.4 - Suppose three fair dice are tossed repeatedly. Let...Ch. 4.4 - Prob. 7QCh. 4.4 - Sometimes the geometric random variable is defined...Ch. 4.4 - Prob. 9QCh. 4.4 - Suppose that the random variables X1 and X2 have...Ch. 4.5 - A door-to-door encyclopedia salesperson is...Ch. 4.5 - An underground military installation is fortified...Ch. 4.5 - Darryls statistics homework last night was to flip...Ch. 4.5 - When a machine is improperly adjusted, it has...Ch. 4.5 - For a negative binomial random variable whose pdf...Ch. 4.5 - Let the random variable X denote the number of...Ch. 4.5 - Calculate the mean, variance, and...Ch. 4.5 - Let X1,X2, and X3 be three independent negative...Ch. 4.5 - Differentiate the moment-generating function...Ch. 4.5 - Suppose that X1,X2,...,Xk are independent negative...Ch. 4.6 - An Arctic weather station has three electronic...Ch. 4.6 - A service contact on a new university computer...Ch. 4.6 - Suppose a set of measurements Y1,Y2,...,Y100 is...Ch. 4.6 - Demonstrate that plays the role of a scale...Ch. 4.6 - Show that a gamma pdf has the unique mode r1; that...Ch. 4.6 - Prove that (12)=. (Hint: Consider E(Z2)), where Z...Ch. 4.6 - Show that (72)=158.Ch. 4.6 - If the random variable Y has the gamma pdf with...Ch. 4.6 - Differentiate the gamma moment-generating function...Ch. 4.6 - Prob. 10Q
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