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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Estimation

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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Chapter 5.2, Problem 11Q

Find the maximum likelihood estimate for θ in the pdf

f Y ( y ; θ ) = 2 y 1 − θ 2 , θ ≤ y ≤ 1

if a random sample of size 6 yielded the measurements 0.70, 0.63, 0.92, 0.86, 0.43, and 0.21.

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 5.2, Problem 10Q

Chapter 5.2, Problem 12Q

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Chapter 5 Solutions

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

Ch. 5.2 - A random sample of size...Ch. 5.2 - The number of red chips and white chips in an urn...Ch. 5.2 - Use the sample y1=8.2,y2=9.1,y3=10.6, and y4=4.9...Ch. 5.2 - Suppose a random sample of size n is drawn from...Ch. 5.2 - Given that y1=2.3,y2=1.9, and y3=4.6 is a random...Ch. 5.2 - Use the method of maximum likelihood to estimate ...Ch. 5.2 - An engineer is creating a project scheduling...Ch. 5.2 - The following data show the number of occupants in...Ch. 5.2 - For the Major League Baseball seasons from 1950...Ch. 5.2 - (a) Based on the random sample...

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Find the maximum likelihood estimate for θ in the pdf f Y ( y ; θ ) = 2 y 1 − θ 2 , θ ≤ y ≤ 1 if a random sample of size 6 yielded the measurements 0.70, 0.63, 0.92, 0.86, 0.43, and 0.21.

Solution Summary: The author calculates the maximum likelihood estimate for theta in the pdf.

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Chapter 5 Solutions