EBK USING & UNDERSTANDING MATHEMATICS
7th Edition
ISBN: 8220106844434
Author: Briggs
Publisher: PEARSON
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Chapter 1.B, Problem 5E
To determine
Make a truth table for each of the following: p and q; p or q; if p, then q. Explain all the truth values in the tables.
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The OU process studied in the previous problem is a common model for interest rates.
Another common model is the CIR model, which solves the SDE:
dX₁ = (a = X₁) dt + σ √X+dWt,
-
under the condition Xoxo. We cannot solve this SDE explicitly.
=
(a) Use the Brownian trajectory simulated in part (a) of Problem 1, and the Euler
scheme to simulate a trajectory of the CIR process. On a graph, represent both the
trajectory of the OU process and the trajectory of the CIR process for the same
Brownian path.
(b) Repeat the simulation of the CIR process above M times (M large), for a large
value of T, and use the result to estimate the long-term expectation and variance
of the CIR process. How do they compare to the ones of the OU process?
Numerical application: T = 10, N = 500, a = 0.04, x0 = 0.05, σ = 0.01, M = 1000.
1
(c) If you use larger values than above for the parameters, such as the ones in Problem
1, you may encounter errors when implementing the Euler scheme for CIR. Explain
why.
Refer to page 1 for a problem involving proving the distributive property of matrix
multiplication.
Instructions: Provide a detailed proof using matrix definitions and element-wise operations.
Show all calculations clearly.
Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]
Refer to page 30 for a problem requiring solving a nonhomogeneous differential equation
using the method of undetermined coefficients.
Instructions: Solve step-by-step, including the complementary and particular solutions. Clearly
justify each step.
Link [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]
Chapter 1 Solutions
EBK USING & UNDERSTANDING MATHEMATICS
Ch. 1.A - Prob. 1QQCh. 1.A - A fallacy is a. a statement that is untrue. b. a...Ch. 1.A - Which of the following could not qualify as a...Ch. 1.A - An argument in which the conclusion essentially...Ch. 1.A - The fallacy of appeal to ignorance occurs when a....Ch. 1.A - Consider the argument ‘‘I don’t support the...Ch. 1.A - Consider again the argument ‘‘I don’t support the...Ch. 1.A - Prob. 8QQCh. 1.A - Suppose that the fact that an event A occurs...Ch. 1.A - When we speak of a straw man in an argument, we...
Ch. 1.A - What is logic? Briefly explain how logic can be...Ch. 1.A - How do we define an argument? What is the basic...Ch. 1.A - What is a fallacy? Choose three examples of...Ch. 1.A - Prob. 4ECh. 1.A - Prob. 5ECh. 1.A - I persuaded my father that I was right with a...Ch. 1.A - I didn’t believe the premises on which he based...Ch. 1.A - Prob. 8ECh. 1.A - I disagree with your conclusion, so your argument...Ch. 1.A - Even though your argument contains a fallacy, your...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - 11-20: Analyzing Fallacies. Consider the following...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - 11-20: Analyzing Fallacies. Consider the following...Ch. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 16ECh. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 18ECh. 1.A - Analyzing Fallacies. Consider the following...Ch. 1.A - Prob. 20ECh. 1.A - Media Claims. Each of the following claims can...Ch. 1.A - Prob. 22ECh. 1.A - Prob. 23ECh. 1.A - Prob. 24ECh. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Prob. 29ECh. 1.A - Prob. 30ECh. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Prob. 32ECh. 1.A - Prob. 33ECh. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Recognizing Fallacies. In the following arguments,...Ch. 1.A - Prob. 36ECh. 1.A - Prob. 37ECh. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - 25-40: Recognizing Fallacies. In the following...Ch. 1.A - Prob. 41ECh. 1.A - Prob. 42ECh. 1.A - Additional Fallacies. Consider the blowing...Ch. 1.A - Additional Fallacies. Consider the blowing...Ch. 1.A - Evaluating Media Information. Choose a current...Ch. 1.A - Snopes. Visit the Snopes.com website and choose...Ch. 1.A - Prob. 47ECh. 1.A - Prob. 48ECh. 1.A - Fallacies in Politics. Discuss the tactics used by...Ch. 1.A - Prob. 50ECh. 1.A - 51. Comment Fallacies. The “reader comments” that...Ch. 1.A - 52. Fake News Sites. Visit a fake news site that...Ch. 1.B - The statement Mathematics is fun is a. an...Ch. 1.B - Suppose you know the truth value of a proposition...Ch. 1.B - Which of the following has the form of a...Ch. 1.B - Suppose you want to make a truth table for the...Ch. 1.B - Suppose the statement p or q is true. Then you can...Ch. 1.B - Suppose the statement p is false and the statement...Ch. 1.B - The statement If it’s a dog, then it is a mammal...Ch. 1.B - The statement If the engine is running, then the...Ch. 1.B - Two statements are logically equivalent if a. they...Ch. 1.B - Prob. 10QQCh. 1.B - What is a proposition? Give a few examples, and...Ch. 1.B - What do we mean by the negation of a proposition?...Ch. 1.B - Define conjunction, disjunction, and conditional,...Ch. 1.B - 4. What is the difference between an inclusive or...Ch. 1.B - 5. Make a truth table for each of the following: p...Ch. 1.B - Prob. 6ECh. 1.B - 7. My logical proposition is a question that you...Ch. 1.B - The mayor opposes repealing the ban on handguns,...Ch. 1.B - Prob. 9ECh. 1.B - Prob. 10ECh. 1.B - Prob. 11ECh. 1.B - Prob. 12ECh. 1.B - Prob. 13ECh. 1.B - Prob. 14ECh. 1.B - 13-18: A proposition? Determine whether the...Ch. 1.B - Prob. 16ECh. 1.B - Prob. 17ECh. 1.B - Prob. 18ECh. 1.B - Negation. Write the negation of the given...Ch. 1.B - Prob. 20ECh. 1.B - Prob. 21ECh. 1.B - Prob. 22ECh. 1.B - Prob. 23ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Prob. 25ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Prob. 27ECh. 1.B - Multiple Negations. Explain the meaning of the...Ch. 1.B - Truth Tables. Make a truth table for the given...Ch. 1.B - Prob. 30ECh. 1.B - Prob. 31ECh. 1.B - And Statements. The following propositions have...Ch. 1.B - Prob. 33ECh. 1.B - And Statements. The following statements have the...Ch. 1.B - Prob. 35ECh. 1.B - 31-36: And Statements. The following statements...Ch. 1.B - Truth Tables. Make a truth table for the given...Ch. 1.B - 37-38: Truth Tables. Make a truth table for the...Ch. 1.B - Prob. 39ECh. 1.B - 39-44: Interpreting or. State whether or is used...Ch. 1.B - Prob. 41ECh. 1.B - Interpreting or. State whether or is used in the...Ch. 1.B - 39-44: Interpreting or. State whether or is used...Ch. 1.B - Interpreting or. State whether or is used in the...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Truth Table. Make a truth table for the given...Ch. 1.B - Prob. 50ECh. 1.B - Prob. 51ECh. 1.B - Prob. 52ECh. 1.B - Prob. 53ECh. 1.B - Prob. 54ECh. 1.B - Prob. 55ECh. 1.B - 51-56: Or Statements. The following statements...Ch. 1.B - 57-58: Truth Tables. Make a truth table for the...Ch. 1.B - 57-58: Truth Tables. Make a truth table for the...Ch. 1.B - Prob. 59ECh. 1.B - Prob. 60ECh. 1.B - Prob. 61ECh. 1.B - Prob. 62ECh. 1.B - If... then Statements. Identify the hypothesis and...Ch. 1.B - Prob. 64ECh. 1.B - Prob. 65ECh. 1.B - If... then Statements. Identify the hypothesis and...Ch. 1.B - Rephrasing Conditional Statements. Express the...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - 67-72: Rephrasing Conditional Statements. Express...Ch. 1.B - Prob. 71ECh. 1.B - Prob. 72ECh. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Prob. 76ECh. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Converse, Inverse, and Contrapositive. Write the...Ch. 1.B - Prob. 79ECh. 1.B - Prob. 80ECh. 1.B - 79-82: Famous Quotes. Rephrase the following...Ch. 1.B - 79-82: Famous Quotes. Rephrase the following...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - Prob. 84ECh. 1.B - Writing Conditional Propositions. Create your own...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - 83-87: Writing Conditional Propositions. Create...Ch. 1.B - Prob. 88ECh. 1.B - Necessary and Sufficient. Write the following...Ch. 1.B - Necessary and Sufficient. Write the following...Ch. 1.B - Prob. 91ECh. 1.B - 89-92: Necessary and Sufficient. Write the...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Prob. 96ECh. 1.B - Logical Equivalence. Consider the following pairs...Ch. 1.B - Prob. 98ECh. 1.B - Prob. 99ECh. 1.B - Prob. 100ECh. 1.B - Prob. 101ECh. 1.B - Prob. 102ECh. 1.C - Consider the set {Alabama, Alaska, Arizona,…,...Ch. 1.C - Which of the following is not a member of the set...Ch. 1.C - Based on the Venn diagram below, we conclude that...Ch. 1.C - Suppose that A represents the set of all boys and...Ch. 1.C - Suppose that A represents the set of all apples...Ch. 1.C - Suppose that A represents the set of all high...Ch. 1.C - In the Venn diagram below, the X tells us that a....Ch. 1.C - Prob. 8QQCh. 1.C - Consider again the Venn diagram from Exercise 8....Ch. 1.C - Look at the data in Table 1.1 (p.34). The total...Ch. 1.C - Prob. 1ECh. 1.C - What is a Venn diagram? How do we show that one...Ch. 1.C - List the four standard categorical propositions....Ch. 1.C - Briefly discuss how you can put a categorical...Ch. 1.C - Explain how to draw a Venn diagram for three...Ch. 1.C - 6. Explain how to read a table such as Table 1.1...Ch. 1.C - The people who live in Chicago form a subset of...Ch. 1.C - All jabbers are wocks, so there must be no wocks...Ch. 1.C - I counted an irrational number of students in my...Ch. 1.C - I surveyed my class to find out whether students...Ch. 1.C - My professor asked me to draw a Venn diagram for a...Ch. 1.C - I used a Venn diagram with three circles to show...Ch. 1.C - Classifying Numbers. Choose the first set in the...Ch. 1.C - Prob. 14ECh. 1.C - Classifying Numbers. Choose the first set in the...Ch. 1.C - Prob. 16ECh. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - 13-28: Classifying Numbers. Choose the first set...Ch. 1.C - Prob. 20ECh. 1.C - Prob. 21ECh. 1.C - Prob. 22ECh. 1.C - Prob. 23ECh. 1.C - Prob. 24ECh. 1.C - Prob. 25ECh. 1.C - Prob. 26ECh. 1.C - Prob. 27ECh. 1.C - Prob. 28ECh. 1.C - Prob. 29ECh. 1.C - Prob. 30ECh. 1.C - Prob. 31ECh. 1.C - Prob. 32ECh. 1.C - Prob. 33ECh. 1.C - Prob. 34ECh. 1.C - Prob. 35ECh. 1.C - Prob. 36ECh. 1.C - Prob. 37ECh. 1.C - Prob. 38ECh. 1.C - Prob. 39ECh. 1.C - Venn Diagrams for Two Sets. Draw Venn diagrams...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - 37-44: Venn Diagrams for Two Sets. Draw Venn...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - 45-52: Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Categorical Propositions. For the given...Ch. 1.C - Prob. 53ECh. 1.C - Prob. 54ECh. 1.C - Prob. 55ECh. 1.C - Prob. 56ECh. 1.C - Prob. 57ECh. 1.C - Prob. 58ECh. 1.C - Prob. 59ECh. 1.C - Prob. 60ECh. 1.C - Two-Circle Venn Diagram with Numbers. Use the Venn...Ch. 1.C - Two-Circle Venn Diagram with Numbers. Use the Venn...Ch. 1.C - Three-Circle Venn Diagram with Numbers. Use the...Ch. 1.C - Three-Circle Venn Diagram with Numbers. Use the...Ch. 1.C - Hospital Drug Use. The following numbers of...Ch. 1.C - Technology Survey. A survey of 150 college...Ch. 1.C - Venn Diagram Analysis. 67. A movie critic reviewed...Ch. 1.C - Venn Diagram Analysis. 68. All runners who...Ch. 1.C - Venn Diagram Analysis. 69. One hundred people who...Ch. 1.C - Venn Diagram Analysis. 70. In a trial of a new...Ch. 1.C - Prob. 71ECh. 1.C - Prob. 72ECh. 1.C - Prob. 73ECh. 1.C - Prob. 74ECh. 1.C - 86. Categorical Propositions. Find at least three...Ch. 1.C - Prob. 76ECh. 1.C - Prob. 77ECh. 1.C - Prob. 78ECh. 1.C - Prob. 79ECh. 1.C - Prob. 80ECh. 1.C - Prob. 81ECh. 1.C - State Politics. Find out how many states have a...Ch. 1.C - Prob. 83ECh. 1.D - To prove a statement true, you must use a. an...Ch. 1.D - If a deductive argument is valid, its conclusion...Ch. 1.D - Prob. 3QQCh. 1.D - 4. Consider an argument in which Premise 1 is "All...Ch. 1.D - 5. Consider again the argument from question 4....Ch. 1.D - Consider an argument in which Premise 1 is “ If p,...Ch. 1.D - 7. Consider an argument in which Premise 1 is “ If...Ch. 1.D - Prob. 8QQCh. 1.D - 9. The longest side of a right triangle is called...Ch. 1.D - Prob. 10QQCh. 1.D - Summarize the differences between deductive and...Ch. 1.D - Briefly explain the idea of strength and how it...Ch. 1.D - Briefly explain the ideas of validity and...Ch. 1.D - Describe the procedure used to test the validity...Ch. 1.D - Prob. 5ECh. 1.D - What is a chain of conditionals? Give an example...Ch. 1.D - Prob. 7ECh. 1.D - Prob. 8ECh. 1.D - 9. My inductive argument provides absolute proof...Ch. 1.D - Prob. 10ECh. 1.D - 11. My argument is deductively valid, so if you...Ch. 1.D - Prob. 12ECh. 1.D - Prob. 13ECh. 1.D - Prob. 14ECh. 1.D - Prob. 15ECh. 1.D - Prob. 16ECh. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Argument Type. Explain whether the following...Ch. 1.D - Prob. 22ECh. 1.D - Prob. 23ECh. 1.D - Prob. 24ECh. 1.D - Prob. 25ECh. 1.D - Prob. 26ECh. 1.D - Prob. 27ECh. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Prob. 30ECh. 1.D - 29-36: Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Analyzing Deductive Arguments. Consider the...Ch. 1.D - Prob. 35ECh. 1.D - Prob. 36ECh. 1.D - Prob. 37ECh. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - 37-44: Deductive Arguments with Conditional...Ch. 1.D - Prob. 41ECh. 1.D - Prob. 42ECh. 1.D - Prob. 43ECh. 1.D - Deductive Arguments with Conditional Propositions....Ch. 1.D - Prob. 45ECh. 1.D - Prob. 46ECh. 1.D - Prob. 47ECh. 1.D - Prob. 48ECh. 1.D - Prob. 49ECh. 1.D - Prob. 50ECh. 1.D - Testing Mathematical Rules. Test the following...Ch. 1.D - It is true for all positive integers n that...Ch. 1.D - 53-57: Validity and Soundness. State whether it is...Ch. 1.D - 53-57: Validity and Soundness. State whether it is...Ch. 1.D - Prob. 55ECh. 1.D - Prob. 56ECh. 1.D - Validity and Soundness. State whether it is...Ch. 1.D - Prob. 58ECh. 1.D - Prob. 59ECh. 1.D - Prob. 60ECh. 1.D - Prob. 61ECh. 1.D - Prob. 62ECh. 1.D - Conditionals in Books. Consider the following...Ch. 1.D - Prob. 64ECh. 1.D - 63-66: Conditionals in Books. Consider the...Ch. 1.D - 63-66: Conditionals in Books. Consider the...Ch. 1.D - 62. The Goldbach Conjecture. Recall that a prime...Ch. 1.D - Twin Primes Conjecture. If you write out the first...Ch. 1.D - The Pythagorean Theorem. Learn more about the...Ch. 1.D - Prob. 70ECh. 1.D - 69. Inductive Reasoning in Your Life. Give an...Ch. 1.D - Prob. 72ECh. 1.D - Prob. 73ECh. 1.D - Prob. 74ECh. 1.E - What does it mean to think critically about the...Ch. 1.E - "If you want to save the social services that...Ch. 1.E - 2. Suppose that an argument is deductively valid...Ch. 1.E - 9. A teacher claims that, because spell checkers...Ch. 1.E - 3. You need to buy a car and are considering loans...Ch. 1.E - 4. You get your hair cut at a shop that charges...Ch. 1.E - You buy a cell phone plan that gives you up to...Ch. 1.E - Prob. 8QQCh. 1.E - Prob. 9QQCh. 1.E - The Smiths have a picnic every Saturday provided t...Ch. 1.E - Describe critical thinking and why it is important...Ch. 1.E - Prob. 2ECh. 1.E - Prob. 3ECh. 1.E - Prob. 4ECh. 1.E - Reed was relieved because his insurance company...Ch. 1.E - 6. Although the plane crashed in Nevada, the...Ch. 1.E - Sue prefers the Red shuttle because it gets her to...Ch. 1.E - Prob. 8ECh. 1.E - There was no price difference, so Michael chose...Ch. 1.E - Prob. 10ECh. 1.E - Prob. 11ECh. 1.E - Interpreting Policies. A city charters sole policy...Ch. 1.E - Reading a Ballot Initiative. Consider the...Ch. 1.E - Prob. 14ECh. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - Prob. 16ECh. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - Hidden Assumptions. Identify at least two hidden...Ch. 1.E - 29-30: Unstated Issues. The following arguments...Ch. 1.E - Unstated Issues. The following arguments give...Ch. 1.E - Airline Options. In planning a trip to New Zealand...Ch. 1.E - Buy vs. Lease. You are deciding whether to buy a...Ch. 1.E - You've Won! You receive the following e-mail...Ch. 1.E - Reading a Lease. Consider the following excerpt...Ch. 1.E - Prob. 25ECh. 1.E - Prob. 26ECh. 1.E - Prob. 27ECh. 1.E - 27-28. Fake News. The following are fake news...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - Prob. 30ECh. 1.E - Prob. 31ECh. 1.E - Prob. 32ECh. 1.E - Prob. 33ECh. 1.E - Prob. 34ECh. 1.E - Prob. 35ECh. 1.E - Prob. 36ECh. 1.E - Prob. 37ECh. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - 29-40: Read and Think Carefully. The following...Ch. 1.E - Decision Making. Analyze the situations. and...Ch. 1.E - Prob. 42ECh. 1.E - Prob. 43ECh. 1.E - Prob. 44ECh. 1.E - IRS Guidelines on Who Must File a Federal Tax...Ch. 1.E - Prob. 46ECh. 1.E - Credit Card Agreement. The following rules are...Ch. 1.E - Prob. 48ECh. 1.E - Texas Ethics. In its Guide to Ethics the Texas...Ch. 1.E - Prob. 50ECh. 1.E - 50-54: Critical Thinking. Consider the following...Ch. 1.E - 57-65: Critical Thinking. Consider the following...Ch. 1.E - 50-54: Critical Thinking. Consider the following...Ch. 1.E - Prob. 54ECh. 1.E - Prob. 55ECh. 1.E - Interpreting the Second Amendment. Much of the...Ch. 1.E - Prob. 57ECh. 1.E - Prob. 58ECh. 1.E - Prob. 59ECh. 1.E - Prob. 60ECh. 1.E - Prob. 61ECh. 1.E - Conspiracy Theories. Choose some well-known...
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- #8 (a) Find the equation of the tangent line to y = √x+3 at x=6 (b) Find the differential dy at y = √x +3 and evaluate it for x=6 and dx = 0.3arrow_forwardRefer to page 96 for a problem involving the heat equation. Solve the PDE using the method of separation of variables. Derive the solution step-by-step, including the boundary conditions. Instructions: Stick to solving the heat equation. Show all intermediate steps, including separation of variables, solving for eigenvalues, and constructing the solution. Irrelevant explanations are not allowed. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardQ.2 Q.4 Determine ffx dA where R is upper half of the circle shown below. x²+y2=1 (1,0)arrow_forward
- Refer to page 83 for a vector field problem requiring verification of conservative nature and finding a scalar potential function. Instructions: Focus strictly on verifying conditions for conservativeness and solving for the potential function. Show all work step-by-step. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440AZF/view?usp=sharing]arrow_forward1000 1500 2000 Quarterly sales of videos in the Leeds "Disney" store are shown in figure 1. Below is the code and output for an analysis of these data in R, with the sales data stored in the time series object X. Explain what is being done at points (i)-(iv) in the R code. Explain what is the difference between (v) and (vi) in the R code. Explain, giving reasons, which of (v) and (vi) is preferable. Write out the model with estimated parameters in full. (The relevant points in the R code are denoted #2#2#3#23 (i) #### etc.) Given that the sales for the four quarters of 2018 were 721, 935, 649, and 1071, use model-based forecasting to predict sales for the first quarter of 2019. (A point forecast is sufficient; you do not need to calculate a prediction interval.) Suggest one change to the fitted model which would improve the analysis. (You can assume that the choice of stochastic process at (v) in the R code is the correct one for these data.) 2010 2012 2014 Time 2016 Figure 1:…arrow_forward2. Let {X} be a moving average process of order q (usually written as MA(q)) defined on tЄ Z as where {et} is a white noise process with variance 1. (1) (a) Show that for any MA(1) process with B₁ 1 there exists another MA(1) pro- cess with the same autocorrelation function, and find the lag 1 moving average coefficient (say) of this process. (b) For an MA(2) process, equation (1) becomes X=&t+B₁et-1+ B2ɛt-2- (2) i. Define the backshift operator B, and write equation (2) in terms of a polyno- mial function B(B), giving a clear definition of this function. ii. Hence show that equation (2) can be written as an infinite order autoregressive process under certain conditions on B(B), clearly stating these conditions.arrow_forward
- explain the importance of the Hypothesis test in a business setting, and give an example of a situation where it is helpful in business decision making.arrow_forwardRefer to page 92 for a problem involving solving coupled first-order ODEs using Laplace transforms. Instructions: Solve step-by-step using Laplace transforms. Show detailed algebraic manipulations and inversions. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS31Z9qoHazb9tC440 AZF/view?usp=sharing] Refer to page 86 for a problem involving solving Legendre's differential equation. Instructions: Solve using power series or standard solutions. Clearly justify every step and avoid unnecessary explanations. Link: [https://drive.google.com/file/d/1wKSrun-GlxirS3IZ9qoHazb9tC440AZF/view?usp=sharing]arrow_forwardConsider the time series model X₁ = u(t)+s(t) + εt. Assuming the standard notation used in this module, what do each of the terms Xt, u(t), s(t) and & represent? In a plot of X against t, what features would you look for to determine whether the terms μ(t) and s(t) are required? Explain why μ(t) and s(t) are functions of t, whilst t is a subscript in X and εt.arrow_forward
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