Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
13th Edition
ISBN: 9780321947628
Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen
Publisher: PEARSON
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Chapter 10.2, Problem 21E
Solve the matrix games in Problems
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Module Code: MATH380202
3. (a) Let {} be a white noise process with variance σ2.
Define an ARMA(p,q) process {X} in terms of {+} and state (without proof)
conditions for {X} to be (i) weakly stationary and (ii) invertible.
Define what is meant by an ARIMA (p, d, q) process. Let {Y} be such an ARIMA(p, d, q)
process and show how it can also be represented as an ARMA process, giving the
AR and MA orders of this representation.
(b) The following tables show the first nine sample autocorrelations and partial auto-
correlations of X and Y₁ = VX+ for a series of n = 1095 observations. (Notice
that the notation in this part has no relationship with the notation in part (a) of
this question.)
Identify a model for this time series and obtain preliminary estimates for the pa-
rameters of your model.
X₁
= 15.51, s² = 317.43.
k
1
2
3
4
5
6
7
Pk
0.981
0.974
0.968
akk 0.981 0.327
8
9
0.927
0.963 0.957 0.951 0.943 0.935
0.121 0.104 0.000 0.014 -0.067 -0.068 -0.012
Y₁ = VX : y = 0.03, s² = 11.48.
k
1…
Let G be a graph with n ≥ 2 vertices x1, x2, . . . , xn, and let A be the adjacency matrixof G. Prove that if G is connected, then every entry in the matrix A^n−1 + A^nis positive.
Module Code: MATH380202
1. (a) Define the terms "strongly stationary" and "weakly stationary".
Let {X} be a stochastic process defined for all t € Z. Assuming that {X+} is
weakly stationary, define the autocorrelation function (acf) Pk, for lag k.
What conditions must a process {X+) satisfy for it to be white noise?
(b) Let N(0, 1) for t€ Z, with the {+} being mutually independent. Which of
the following processes {X+} are weakly stationary for t> 0? Briefly justify your
answers.
i. Xt for all > 0.
ii. Xo~N(0,) and X₁ = 2X+-1+ &t for t > 0.
(c) Provide an expression for estimating the autocovariance function for a sample
X1,..., X believed to be from a weakly stationary process. How is the autocor-
relation function Pk then estimated, and a correlogram (or acf plot) constructed?
(d) Consider the weakly stationary stochastic process ✗+ = + + +-1+ +-2 where
{E} is a white noise process with variance 1. Compute the population autocorre-
lation function Pk for all k = 0, 1, ....
Chapter 10 Solutions
Finite Mathematics for Business, Economics, Life Sciences and Social Sciences Plus NEW MyLab Math with Pearson eText -- Access Card Package (13th Edition)
Ch. 10.1 - Suppose that a and k are both saddle values of the...Ch. 10.1 - Repeat Example 1 for the HDTV game matrix...Ch. 10.1 - Determine which of the matrix games below are...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 1-8, is the matrix game strictly...
Ch. 10.1 - In Problems 1-8, is the matrix game strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - In Problems 916, the matrix for a strictly...Ch. 10.1 - Prob. 17ECh. 10.1 - Prob. 18ECh. 10.1 - Prob. 19ECh. 10.1 - Prob. 20ECh. 10.1 - Prob. 21ECh. 10.1 - Prob. 22ECh. 10.1 - Prob. 23ECh. 10.1 - Prob. 24ECh. 10.1 - Prob. 25ECh. 10.1 - Prob. 26ECh. 10.1 - Prob. 27ECh. 10.1 - Prob. 28ECh. 10.1 - Prob. 29ECh. 10.1 - Prob. 30ECh. 10.1 - Prob. 31ECh. 10.1 - Prob. 32ECh. 10.1 - For the matrix game of Problem 31, would you...Ch. 10.1 - For the matrix game of Problem 32, would you...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - In Problems 35-40, discuss the validity of each...Ch. 10.1 - Is there a value of m such that the following is...Ch. 10.1 - Prob. 42ECh. 10.1 - Price war a small town on a major highway has only...Ch. 10.1 - Investment Suppose that you want to invest $10,000...Ch. 10.1 - Store location two competitive pet shops want to...Ch. 10.1 - Store location Two competing auto parts companies...Ch. 10.2 - Let M=abcd (A) Show that if the row minima belong...Ch. 10.2 - (A) Using Theorem 4, give conditions on a,b,c, and...Ch. 10.2 - Solve the following version of the two-finger...Ch. 10.2 - Solve the matrix game: M=112324113Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 1-8, calculate the matrix product. (If...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - In Problems 9-18, which rows and columns of the...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - Solve the matrix games in Problems 1932,...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - In Problems 33-38, discuss the validity of each...Ch. 10.2 - You R and a friend C are playing the following...Ch. 10.2 - You R and a friend C are playing the following...Ch. 10.2 - For M=abcdP=p1p2Q=q1q2 Show that PMQ=EP,QCh. 10.2 - Using the fundamental theorem of game theory,...Ch. 10.2 - Show non strictly that the determined solution...Ch. 10.2 - Show that if a 22 matrix game has a saddle value,...Ch. 10.2 - Explain how to construct a 22 matrix game M for...Ch. 10.2 - Explain how to construct a 22 matrix game M for...Ch. 10.2 - In Problems 47 and 48, derive the formulas of...Ch. 10.2 - In Problems 47 and 48, derive the formulas of...Ch. 10.2 - Bank promotion A town has only two banks, bank R...Ch. 10.2 - Viewer ratings A city has two competitive...Ch. 10.2 - Investment You have inherited $10,000 just prior...Ch. 10.2 - Corporate farming For a one-time play...Ch. 10.3 - Show that M=1132 is a strictly determined matrix...Ch. 10.3 - Solve the following matrix game using geometric...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 1-6, find the smallest integer k0 such...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - In problem 7-12, solve the matrix game using a...Ch. 10.3 - Is there a better way to solve the matrix game in...Ch. 10.3 - Is there a better way to solve the matrix game in...Ch. 10.3 - Explain why the value of a matrix game is positive...Ch. 10.3 - Explain why the value of a matrix game is negative...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In the Problems 1722, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In the Problems 1722, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In Problem 17-20, discuss the validity of each...Ch. 10.3 - In Problems 23 and 24 remove recessive rows and...Ch. 10.3 - In Problems 23 and 24 remove recessive rows and...Ch. 10.3 - (A) Let P and Q be strategies for the 22 matrix...Ch. 10.3 - Use properties of matrix addition and...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.3 - Solve the matrix games in problems 27-30 by using...Ch. 10.4 - Outline a procedure for solving the 45 matrix game...Ch. 10.4 - Suppose that the investor in Example 1 wishes to...Ch. 10.4 - In Problems 1-4, solve each matrix game 140012Ch. 10.4 - In Problems 1-4, solve each matrix game. 112201Ch. 10.4 - In Problems 1-4, solve each matrix game. 012103230Ch. 10.4 - In Problems 1-4, solve each matrix game. 120012201Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - In Problems 5-8, outline a procedure for solving...Ch. 10.4 - Scissors, paper ,stone game This game is well...Ch. 10.4 - Player R has a $2, a $5,and a $10 bill. Player C...Ch. 10.4 - Headphone sales. A department store chain is about...Ch. 10.4 - Tour agency A tour agency organizes standard and...Ch. 10 - In Problems 1 and 2, is the matrix game strictly...Ch. 10 - In Problems 1 and 2, is the matrix game strictly...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - In Problems 3-8, determine the value V of the...Ch. 10 - Prob. 9RECh. 10 - Prob. 10RECh. 10 - Prob. 11RECh. 10 - Prob. 12RECh. 10 - Delete as many recessive rows and columns as...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - Problems 14-17 refer to the matrix game: M=2101...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 18-21, discuss the validity of each...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - In Problems 22-26, solve each matrix game (first...Ch. 10 - Does every strictly determined 22 matrix game have...Ch. 10 - Does every strictly determined 33 matrix game have...Ch. 10 - Finger game Consider the following finger game...Ch. 10 - Refer to Problem 29. Use linear programming and a...Ch. 10 - Agriculture A farmer decides each spring whether...Ch. 10 - Agriculture Refer to Problem 31. Use formulas from...Ch. 10 - Advertising A small town has two competing grocery...Ch. 10 - Advertising Refer to Problem 33. Use linear...
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