Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

14th Edition

ISBN: 9780134677972

Author: Barnett

Publisher: PEARSON

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Textbook Question

Chapter 8.1, Problem 70E

(A) Is it possible to get 7 double 6 ' s in 10 rolls of a pair of fair dice? Explain.

(B) If you rolled a pair of dice 36 times and got 11 double 6 ' s , would you suspect that the dice were unfair? Why or why not? If you suspect loaded dice, what empirical probability would you assign to the event of rolling a double 6 ?

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Chapter 8.1, Problem 69E

Chapter 8.1, Problem 71E

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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 8 Solutions

Finite Mathematics for Business, Economics, Life Sciences and Social Sciences

Ch. 8.1 - A shipment box contains 12 graphing calculators,...Ch. 8.1 - Repeat Example 1 for (A) The outcome is a number...Ch. 8.1 - An experiment consists of recording the boy-girl...Ch. 8.1 - Refer to the sample space shown in Figure 2. What...Ch. 8.1 - Suppose in Example 4 that after flipping the...Ch. 8.1 - Under the conditions in Example 5, find the...Ch. 8.1 - Use the graphing calculator output in Figure 4B to...Ch. 8.1 - In drawing 7 cards from a 52 -card deck without...Ch. 8.1 - What is the probability that the committee in...Ch. 8.1 - In Problems 1-6, without using a calculator,...

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