Explanation Given: The sums of the first column of M , and the first column of S M for each player are tabulated below. Player Name Sum of first column of M First column of S M Barry Bonds 5.43012 [ 0.281776 0.292658 0.258525 0.167041 ] Babe Ruth 5.70250 [ 0.268150 0.295908 0.268120 0.167822 ] Ted Williams 5.79929 [ 0.233655 0.276714 0.290207 0.199425 ] Formula used: 1. The expected number of runner left on the base in a typical half-inning: E [ L ] = 0 ⋅ P ( L = 0 ) + 1 ⋅ P ( L = 1 ) + 2 ⋅ P ( L = 2 ) + 3 ⋅ P ( L = 3 ) . 2. The expected number of earned runs scored: E [ R ] = E [ B ] − E [ L ] − 3 . Calculation: The sum of the first column of M for player Barry Bonds is 5.43012, and the first column of S M is. [ 0.281776 0.292658 0.258525 0.167041 ] . The sum of the first column of the matrix M gives the value of E B [ B ] , that is E B [ B ] = 5.43012 . Use, the above Formula 1 and compute the value of E B [ L ] from the values of the first column of S M as follows, E B [ L ] = 0 ⋅ P ( L = 0 ) + 1 ⋅ P ( L = 1 ) + 2 ⋅ P ( L = 2 ) + 3 ⋅ P ( L = 3 ) = 0 ⋅ ( 0.281776 ) + 1 ⋅ ( 0.292658 ) + 2 ⋅ ( 0.258525 ) + 3 ⋅ ( 0.167041 ) = 0 + 0.292658 + 0.51705 + 0.501123 = 1.310831 Thus, the value of E B [ L ] = 1.310831 . Substitute E B [ L ] = 1.310831 , E B [ B ] = 5.43012 in E B [ R ] and evaluate as follows. E B [ R ] = 5.43012 − 1.310831 − 3 = 1.119289 Therefore, the expected number of earned runs per inning by the player Barry Bonds is E B [ R ] = 1.119289 . Similarly, obtain expected number of earned runs per inning by the player Babe Ruth as follows. It is observed that the sum of the first column of M for player Babe Ruth is 5.70250, and the first column of S M is. [ 0.268150 0.295908 0.268120 0.167822 ] . The sum of the first column of the matrix M gives the value of E R [ B ] , that is E R [ B ] = 5

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

5th Edition

ISBN: 9781323132098

Author: Thomas, Lay

Publisher: PEARSON C

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Chapter 10.6, Problem 12E

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To find: The offensive earned run averages of three players and which batter does the model say was the best of these three.

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Chapter 10.6, Problem 11E

Chapter 10.6, Problem 14E

Chapter 10 Solutions

Thomas' Calculus and Linear Algebra and Its Applications Package for the Georgia Institute of Technology, 1/e

Ch. 10.1 - Fill in the missing entries in the stochastic...Ch. 10.1 - Prob. 2PP Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - In Exercises 1 and 2, determine whether P is a...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - In Exercises 5 and 6, the transition matrix P for...Ch. 10.1 - Prob. 6E Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...Ch. 10.1 - In Exercises 7 and 8, the transition matrix P for...

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The offensive earned run averages of three players and which batter does the model say was the best of these three.

Solution Summary: The author calculates the offensive earned run averages of three players and which batter is the best of these three.

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