course1_1101 - November 2001 Course 1 Mathematical...

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November 2001 Course 1 Mathematical Foundations of Actuarial Science Society of Actuaries/Casualty Actuarial Society
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Course 1, November 2001 2 1. An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 . Calculate the number of blue balls in the second urn. (A) 4 (B) 20 (C) 24 (D) 44 (E) 64
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Course 1, November 2001 3 2. Let R be a region in the xy -plane with area 2 . Let R ∫∫ f ( x , y ) dA = 6 . Determine R [4 f ( x , y ) – 2] dA . (A) 12 (B) 18 (C) 20 (D) 22 (E) 44
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Course 1, November 2001 4 3. Sales, S , of a new insurance product are dependent upon the labor, L , of the sales force and the amount of advertising, A , for the product. The relationship can be modeled by S = 175 L 3/2 A 4/5 . Which of the following statements is true? (A) S increases at an increasing rate as L increases and increases at a decreasing rate as A increases. (B) S increases at an increasing rate as L increases and increases at an increasing rate as A increases. (C) S increases at a decreasing rate as L increases and increases at a decreasing rate as A increases. (D) S increases at a decreasing rate as L increases and increases at an increasing rate as A increases. (E) S increases at a constant rate as L increases and increases at a constant rate as A increases.
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Course 1, November 2001 5 4. Upon arrival at a hospital’s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year: (i) 10% of the emergency room patients were critical; (ii) 30% of the emergency room patients were serious; (iii) the rest of the emergency room patients were stable; (iv) 40% of the critical patients died; (vi) 10% of the serious patients died; and (vii) 1% of the stable patients died. Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival? (A) 0.06 (B) 0.29 (C) 0.30 (D) 0.39 (E) 0.64
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Course 1, November 2001 6 5. An insurance company sells a one-year automobile policy with a deductible of 2 . The probability that the insured will incur a loss is 0.05 . If there is a loss, the probability of a loss of amount N is K N , for N = 1, . . . , 5 and K a constant. These are the only possible loss amounts and no more than one loss can occur. Determine the net premium for this policy. (A) 0.031 (B) 0.066 (C) 0.072 (D) 0.110 (E) 0.150
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Course 1, November 2001 7 6. Let C be the curve defined by the parametric equations x = t 2 + t , y = t 2 – 1 . Determine the value of t at which the line tangent to the graph of C is parallel to the line 5 y – 4 x = 3 . (A) 1 10 (B) 2 5 (C) 5 8 (D) 5 3 (E) 2
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Course 1, November 2001 8 7. Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which E( X ) = 5, E( X 2 ) = 27.4, E( Y ) = 7, E( Y 2 ) = 51.4, and Var( X + Y ) = 8 .
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This note was uploaded on 03/27/2012 for the course MATHEMATIC 4523 taught by Professor Zhangqiang during the Spring '12 term at City University of Hong Kong.

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course1_1101 - November 2001 Course 1 Mathematical...

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