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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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.

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Textbook Question

Chapter 10.2, Problem 8Q

Let the vector of random variables ( X 1 , X 2 , X 3 ) have the trinomial pdf with parameters n p 1 , p 2 , a n d p 3 . That is,

P ( X 1 = k 1 , X 2 = k 2 , X 3 = k 3 ) = n ! k 1 ! k 2 ! k 3 ! p 1 k 1 p 2 k 2 p 3 k 3 , k i = 0 , 1 , ..... , n ; i = 1,2,3; k 1 + k 2 + k 3 = n

By definition, the moment-generating function for ( X 1 , X 2 , X 3 ) is given by

M X 1 , X 2 , X 3 ( t 1 , t 2 , t 3 ) = E ( e t 1 X 1 + t 2 X 2 + t 3 X 3 )

Show that

M X 1 , X 1 , X 1 ( t 1 , t 2 , t 3 ) = ( p 1 e t 1 + p 2 e t 2 + p 3 e t 3 ) n

Definition Definition Probability of occurrence of a continuous random variable within a specified range. When the value of a random variable, Y, is evaluated at a point Y=y, then the probability distribution function gives the probability that Y will take a value less than or equal to y. The probability distribution function formula for random Variable Y following the normal distribution is: F(y) = P (Y ≤ y) The value of probability distribution function for random variable lies between 0 and 1.

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Chapter 10.2, Problem 7Q

Chapter 10.2, Problem 9Q

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Chapter 10 Solutions

An Introduction to Mathematical Statistics and Its Applications (6th Edition)

Ch. 10.2 - The Advanced Placement Program allows high school...Ch. 10.2 - In Mendels classical experiments with peas, he...Ch. 10.2 - Prob. 3Q Ch. 10.2 - An army enlistment officer categorizes potential...Ch. 10.2 - A disgruntled Anchorage bush pilot, upset because...Ch. 10.2 - Based on his performance so far this season, a...Ch. 10.2 - Suppose that a random sample of fifty observations...Ch. 10.2 - Let the vector of random variables (X1,X2,X3) have...Ch. 10.2 - Prob. 9Q Ch. 10.2 - Prob. 10Q

Ch. 10.3 - Verify the following identity concerning the...Ch. 10.3 - One hundred unordered samples of size 2 are drawn...Ch. 10.3 - Prob. 3Q Ch. 10.3 - Show that the common belief in the propensity of...Ch. 10.3 - Prob. 5Q Ch. 10.3 - A number of reports in the medical literature...Ch. 10.3 - In a move that shocked candy traditionalists at...Ch. 10.3 - Test at the 0.10 level whether World Series...Ch. 10.3 - Records Kept at an eastern racetrack showed the...Ch. 10.3 - Prob. 10Q Ch. 10.3 - Prob. 11Q Ch. 10.3 - The man () and standard deviation () of pregnancy...Ch. 10.4 - A public policy polling group is investigating...Ch. 10.4 - From 1837 to 1932, the U.S. Supreme Court had...Ch. 10.4 - Prob. 3Q Ch. 10.4 - Carry out the details for goodness-of-fit test on...Ch. 10.4 - Prob. 5Q Ch. 10.4 - Do a goodness-of-fit test for normality on the SAT...Ch. 10.4 - A sociologist is studying various aspects of the...Ch. 10.4 - In theory, Monte Carlo studies rely on computers...Ch. 10.4 - Because it satisfies all the assumptions implicit...Ch. 10.4 - In American football a turnover is defined as a...Ch. 10.4 - Prob. 11Q Ch. 10.4 - To raise money for a new rectory, the members of a...Ch. 10.4 - Prob. 14Q Ch. 10.5 - While there are a number of diet and physical...Ch. 10.5 - Prob. 2Q Ch. 10.5 - A total of 1154 girls attending a public high...Ch. 10.5 - Recall the rubella/birth defect study described in...Ch. 10.5 - Research has suggested that regular use of aspirin...Ch. 10.5 - High blood pressure is known to be one of the...Ch. 10.5 - The following data were collected as part of a...Ch. 10.5 - A university conducted a study to assess...Ch. 10.5 - Some studies have suggested that pilots have an...Ch. 10.5 - Students elect to take Calculus I in different...

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Solution Summary: The author explains that the moment-generating function for (X_1,x­2) is given by

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Solution Summary: The author explains that the moment-generating function for (X_1,x2) is given by