course1_0503

# course1_0503 - May 2003 Course 1 1 A survey of a group's...

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Course 1 6 Form 03A 1. A survey of a group’s viewing habits over the last year revealed the following information: (i) 28% watched gymnastics (ii) 29% watched baseball (iii) 19% watched soccer (iv) 14% watched gymnastics and baseball (v) 12% watched baseball and soccer (vi) 10% watched gymnastics and soccer (vii) 8% watched all three sports. Calculate the percentage of the group that watched none of the three sports during the last year. (A) 24 (B) 36 (C) 41 (D) 52 (E) 60

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May 2003 7 Course 1 2. Each of the graphs below contains two curves. Identify the graph containing a curve representing a function () yfx = and a curve representing its second derivative ( ) ′′ = . (A) (B) (C) (D) (E)
Course 1 8 Form 03A 3. Let f and g be differentiable functions such that ( ) () 0 0 lim lim x x f xc gx d = = where cd . Determine () () 0 lim x cf x dg x f xg x . (A) 0 (B) 00 cf dg fg ′′ (C) (D) (E) +

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May 2003 9 Course 1 4. The time to failure of a component in an electronic device has an exponential distribution with a median of four hours. Calculate the probability that the component will work without failing for at least five hours. (A) 0.07 (B) 0.29 (C) 0.38 (D) 0.42 (E) 0.57
Course 1 10 Form 03A 5. An insurance company examines its pool of auto insurance customers and gathers the following information: (i) All customers insure at least one car. (ii) 70% of the customers insure more than one car. (iii) 20% of the customers insure a sports car. (iv) Of those customers who insure more than one car, 15% insure a sports car. Calculate the probability that a randomly selected customer insures exactly one car and that car is not a sports car. (A) 0.13 (B) 0.21 (C) 0.24 (D) 0.25 (E) 0.30

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May 2003 11 Course 1 6. Let X and Y be continuous random variables with joint density function 8 for 0 1, 2 (, ) 3 0o t h e r w i s e . x yx x y x fxy ≤≤ ≤≤ = Calculate the covariance of X and Y . (A) 0.04 (B) 0.25 (C) 0.67 (D) 0.80 (E) 1.24
Course 1 12 Form 03A 7. () () 24 02 Given 3 and 5, fxd x x == ∫∫ () 2 0 calculate 2 . f xd x (A) 32 (B) 3 (C) 4 (D) 6 (E) 8

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May 2003 13 Course 1 8. An auto insurance company insures drivers of all ages. An actuary compiled the following statistics on the company’s insured drivers: Age of Driver Probability of Accident Portion of Company’s Insured Drivers 16-20 21-30 31-65 66-99 0.06 0.03 0.02 0.04 0.08 0.15 0.49 0.28 A randomly selected driver that the company insures has an accident. Calculate the probability that the driver was age 16-20. (A) 0.13 (B) 0.16 (C) 0.19 (D) 0.23 (E) 0.40
Course 1 14 Form 03A 9. An insurance company determines it cannot write medical malpractice insurance profitably and stops selling the coverage. In spite of this action, the company will have to pay claims for many years on existing medical malpractice policies. The company pays 60 for medical malpractice claims the year after it stops selling the coverage. Each subsequent year’s payments are 20% less than those of the previous year.

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## This note was uploaded on 03/22/2012 for the course MATH Financial taught by Professor Bruce during the Spring '12 term at CUNY Baruch.

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course1_0503 - May 2003 Course 1 1 A survey of a group's...

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