Excursions in Modern Mathematics (9th Edition)
9th Edition
ISBN: 9780134468372
Author: Peter Tannenbaum
Publisher: PEARSON
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Textbook Question
Chapter 8, Problem 50E
Consider the project described by the digraph shown in Fig. 8-39, and assume that you are to schedule this project using
a. Use the decreasing-time algorithm to schedule the project. Show the timeline for the project and finishing time
b. Find an optimal schedule. (Hint:
c. Use the relative error formula
Figure 8-39
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Students have asked these similar questions
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 8 Solutions
Excursions in Modern Mathematics (9th Edition)
Ch. 8 - For the digraph shown in Fig. 8-25, find a.the...Ch. 8 - For the digraph shown in Fig. 8-26, find Figure...Ch. 8 - For the digraph in Fig. 8-25, find a.all path of...Ch. 8 - For the digraph in Fig. 8-26, find a.a path of...Ch. 8 - For the digraph in Fig. 8-25, find a.all cycles of...Ch. 8 - For the digraph in Fig. 8-26, find a.all cycles of...Ch. 8 - Prob. 7ECh. 8 - For the digraph in Fig.8-26, find a.all vertices...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...Ch. 8 - a.Draw a digraph with vertex-set V={A,B,C,D} and...
Ch. 8 - Prob. 11ECh. 8 - Consider the digraph with vertex-set V={V,W,X,Y,Z}...Ch. 8 - Prob. 13ECh. 8 - Prob. 14ECh. 8 - Prob. 15ECh. 8 - A mathematics textbook consists of 10 chapters....Ch. 8 - Prob. 17ECh. 8 - The digraph in Fig. 8-29 is an example of a...Ch. 8 - Prob. 19ECh. 8 - Wobble, a start-up company, is developing a search...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - A project consists of eight tasks labeled A...Ch. 8 - Prob. 23ECh. 8 - Prob. 24ECh. 8 - Prob. 25ECh. 8 - A ballroom is to be set up for a large wedding...Ch. 8 - Prob. 27ECh. 8 - Prob. 28ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 31ECh. 8 - Exercises 29 through 32 refer to a project...Ch. 8 - Prob. 33ECh. 8 - Exercises33 and 34 refer to the Martian Habitat...Ch. 8 - Prob. 35ECh. 8 - Prob. 36ECh. 8 - Prob. 37ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 39ECh. 8 - Using the priority list G,F,E,D,C,B,A, schedule...Ch. 8 - Prob. 41ECh. 8 - Prob. 42ECh. 8 - Prob. 43ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 45ECh. 8 - Use the decreasing-time algorithm to schedule the...Ch. 8 - Prob. 47ECh. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project described by the digraph...Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Consider the project digraph shown in Fig.8-40....Ch. 8 - Prob. 53ECh. 8 - Consider the project digraph shown in Fig.8-41....Ch. 8 - Schedule the Apartments Unlimited project given in...Ch. 8 - Schedule the project given in Exercise26 Table8-5...Ch. 8 - Consider the project described by the project...Ch. 8 - Consider the project digraph shown in Fig.8-43,...Ch. 8 - Prob. 59ECh. 8 - Symmetric and totally asymmetric digraphs. A...Ch. 8 - Prob. 61ECh. 8 - Let W represent the sum of the processing times of...Ch. 8 - You have N=2 processors to process M independent...Ch. 8 - You have N=3 processors to process M independent...Ch. 8 - You have N=2 processor to process M+1 independent...
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