MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
9th Edition
ISBN: 9780136415893
Author: Tannenbaum
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Textbook Question
Chapter 5, Problem 73E
Running
Suppose G is a simple graph with N vertices
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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 5 Solutions
MYLAB MATH FOR EXCURSIONS IN MATHEMATIC
Ch. 5 - For the graph shown in Fig 5-29, a.give the vertex...Ch. 5 - For the graph shown in Fig. 5-30, a.give the...Ch. 5 - For the graph shown in Fig. 5-31, 1.give the...Ch. 5 - For the graph shown in Fig. 5-32, a.give the...Ch. 5 - Consider the graph with vertex set {K,R,S,T,W} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,D,E} and...Ch. 5 - Consider the graph with vertex set {A,B,C,X,Y,Z}...Ch. 5 - a.Give an example of a connected graph with eight...Ch. 5 - a.Give an example of a connected graph with eight...
Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find a path...Ch. 5 - Consider the graph in Fig. 5-33. a. Find all...Ch. 5 - Consider the graph in Fig 5-34 a.Find all circuits...Ch. 5 - List all the bridges in each of the following...Ch. 5 - List all the bridges in each of the following...Ch. 5 - Consider the graph in Fig 5-35. a. List all the...Ch. 5 - Consider the graph in Fig 5-36. a. List all the...Ch. 5 - Figure 5-37 shows a map of the downtown area of...Ch. 5 - Figure 5-38 is a map of downtown Royalton, showing...Ch. 5 - A night watchman must walk the streets of the...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - Six teams (A,B,C,D,E,andF) are entered in a...Ch. 5 - The Kangaroo Lodge of Madison Country has 10...Ch. 5 - Table 5-3 summarizes the Facebook friendships...Ch. 5 - The Dean of students office wants to know how the...Ch. 5 - Figure 5-40 shows the downtown area of the small...Ch. 5 - Prob. 28ECh. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercises 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - In Exercise 29 through 34 choose from the...Ch. 5 - Find the Euler circuit for the graph in Fig.5-47....Ch. 5 - Find the Euler circuit for the graph in Fig.5.48_....Ch. 5 - Find the Euler path for the graph in Fig.5-49_....Ch. 5 - Find the Euler path for the graph in Fig.5-50....Ch. 5 - Find an Euler circuit for the graph in Fig 5-51....Ch. 5 - Find the Euler circuit for the graph in Fig 5-52....Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Suppose you are using Fleurys algorithm to find an...Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig....Ch. 5 - Find an optimal eulerization for the graph in Fig...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Find an optimal semi-eulerization for the graph in...Ch. 5 - Prob. 49ECh. 5 - Prob. 50ECh. 5 - Prob. 51ECh. 5 - Prob. 52ECh. 5 - A security guard must patrol on foot the streets...Ch. 5 - A mail carrier must deliver mail on foot along the...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - This exercise refers to the Fourth of July parade...Ch. 5 - Consider the following puzzle: You must trace Fig...Ch. 5 - a.Explain why in every graph the sum of the...Ch. 5 - Prob. 59ECh. 5 - Regular graphs. A graph is called regular if every...Ch. 5 - Suppose G is a disconnected graph with exactly two...Ch. 5 - Consider the following game. You are given N...Ch. 5 - Figure 5-59 shows a map of the downtown area of...Ch. 5 - Kissing circuits. When two circuits in a graph...Ch. 5 - Prob. 65ECh. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - Exercises 66 through 68 refer to Example 5.23 . In...Ch. 5 - This exercise comes to you courtesy of Euler...Ch. 5 - Running Suppose G is a connected graph with N...Ch. 5 - Running Suppose G is a connected graph with N2...Ch. 5 - Running Complete bipartite graphs. A complete...Ch. 5 - Running Suppose G is a simple graph with N...
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