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

14th Edition

ISBN: 9780134677972

Author: Barnett

Publisher: PEARSON

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

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Textbook Question

Chapter 4.1, Problem 73E

Delivery charges. United Express, a national package delivery service, charges a base price for overnight delivery of packages weighing I pound or less and a surcharge for each additional pound (or fraction thereof). A customer is billed $27 .75 for shipping a 5-pound package and $64 .50 for a 20-pound package. Find the base price and the surcharge for each additional pound.

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Chapter 4.1, Problem 72E

Chapter 4.1, Problem 74E

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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…

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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 4 Solutions

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

Ch. 4.1 - Can a consistent and dependent system have exactly...Ch. 4.1 - Return to Example 2 and solve each system by...Ch. 4.1 - Solve by graphing and check: 2xy=3x+2y=4 Ch. 4.1 - Solve each of the following systems by graphing:...Ch. 4.1 - Solve to two decimal places using graphical...Ch. 4.1 - Solve by substitution: 3x3y=22xy=6 Ch. 4.1 - Solve the following system using elimination by...Ch. 4.1 - Dennis wants to use cottage cheese and yogurt to...Ch. 4.1 - Find the equilibrium quantity and equilibrium...Ch. 4.1 - In Problems 1-6, find the x and y coordinates of...

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Solution Summary: The author calculates the base price and the surcharge for United Express shipping service.

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