RMSC2001_Tutorial_6_Solution.pdf - RMSC2001 Introduction to Risk Management Tutorial 6 Midterm Rivision Chen Sihan 1 Risk Exercise 1.1 1 The relative

RMSC2001_Tutorial_6_Solution.pdf - RMSC2001 Introduction to...

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RMSC2001 - Introduction to Risk Management Tutorial 6: Midterm Rivision Chen, Sihan Oct 23, 2019 1 Risk Exercise 1.1. 1. The relative variation between expected losses and actual losses is called (a) subjective probability.(b) objective probability.(c) subjective risk.(d) objective risk. 2. Which of the following statements is (are) true with respect to pure risk?I. Pure risks may produce either a profit or a loss.II. Premature death and damage to property caused by a fire are pure risks. 3. A publishing company solicits manuscripts for publication. The publisher is concernedthat an author might plagiarize material and that the person plagiarized might suethe publisher.To address this risk, the contract with the author includes a hold-harmless agreement. Through this agreement, the author, rather than the publisher,is held liable for plagiarism. In this situation, the publisher is using the hold-harmlessagreement as what type of risk treatment measure? 1
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4. Individuals face the risk of doing something that results in bodily injury or property damage to someone else. A court of law may order the person responsible for the wrongful act to pay damages to the party who was injured. This type of risk is called the (a) liability risk. (b) speculative risk. (c) property risk. (d) fundamental risk. 5. Deans Discount Store has been experiencing problems with shoplifting losses.Deandecided to install a camera monitoring system and to use magnetic price tags onproducts. If the tags are not demagnetized before the product bearing the tags leavesthe store, an alarm bell sounds. These measures are examples of 6. A risk that affects the entire economy, or a large number of persons or groups withinthe economy, is called a(n) (a) particular risk.(b) fundamental risk.(c) speculative risk.(d) objective risk.Solution.1D, 2C, 3B, 4A, 5B, 6B. Exercise 1.2. Suppose the length of the plug (measured in cm) follows a N (6 , 1) distribu- tion. If the length of the plug is bigger than 7.96cm, it will be too large to fit into the socket and a loss of $5 will occur. 1. Find the probability that a loss occurs. 2. If a factory produces 100 plugs, what are the expected loss and the variance of the loss? 3. (Optional) If a factory earns $2 for a plug less than 7.96 cm, at least how many plugs should the company produce so that they can earn $100 with probability greater than 95%? Hint: If Z ∼ N (0 , 1), then P ( Z > 1 . 96) = 0 . 025 and P ( Z > 1 . 645) = 0 . 05. To solve sub-question 3, we are in need of the following theorem: 2
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Theorem 1.1. (Central Limit Theorem) If X 1 , X 2 , . . . are independent r.v.’s, with E X i = μ, V ar ( X i ) = σ 2 (0 , ) , i , then as n → ∞ , ¯ X - μ σ/ n D → N (0 , 1) , where ¯ X = n i =1 X i .
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