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May2003 ExamP

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  • 7/31/2019 May2003 ExamP

    1/40Course 1 6 Form 03A

    1. A survey of a groups 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 sportsduring the last year.

    (A) 24

    (B) 36

    (C) 41

    (D) 52

    (E) 60

    May 2003 - Course 1

  • 7/31/2019 May2003 ExamP

    2/40 May 2003 7 Course 1

    2. Each of the graphs below contains two curves.

    Identify the graph containing a curve representing a function ( ) y f x= and a curve

    representing its second derivative ( ) y f x= .

    (A) (B)

    (C) (D)

    (E)

  • 7/31/2019 May2003 ExamP

    3/40Course 1 8 Form 03A

    3. Let f and g be differentiable functions such that

    ( )( )

    0

    0

    lim

    lim x

    x

    f x c

    g x d

    =

    =

    where c d .

    Determine( ) ( )( ) ( )

    0lim x

    cf x dg x

    f x g x .

    (A) 0

    (B)( ) ( )( ) ( )

    0 0

    0 0

    cf dg

    f g

    (C) ( ) ( )0 0 f g

    (D) c d

    (E) c d +

  • 7/31/2019 May2003 ExamP

    4/40 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

  • 7/31/2019 May2003 ExamP

    5/40Course 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 andthat car is not a sports car.

    (A) 0.13

    (B) 0.21

    (C) 0.24

    (D) 0.25

    (E) 0.30

  • 7/31/2019 May2003 ExamP

    6/40 May 2003 11 Course 1

    6. Let X and Y be continuous random variables with joint density function

    8for 0 1, 2

    ( , ) 30 otherwise.

    y x x y x f x y

    =

    Calculate the covariance of X and Y .

    (A) 0.04

    (B) 0.25

    (C) 0.67

    (D) 0.80

    (E) 1.24

  • 7/31/2019 May2003 ExamP

    7/40Course 1 12 Form 03A

    7. ( ) ( )2 4

    0 2Given 3 and 5, f x dx f x dx= =

    ( )2

    0calculate 2 . f x dx

    (A) 3 2

    (B) 3

    (C) 4

    (D) 6

    (E) 8

  • 7/31/2019 May2003 ExamP

    8/40 May 2003 13 Course 1

    8. An auto insurance company insures drivers of all ages. An actuary compiled the

    following statistics on the companys insured drivers:

    Age of Driver

    Probabilityof Accident

    Portion of CompanysInsured Drivers

    16-2021-3031-6566-99

    0.060.030.020.04

    0.080.150.490.28

    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

  • 7/31/2019 May2003 ExamP

    9/40Course 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 years payments are 20% less than those of the previous year.

    Calculate the total medical malpractice payments that the company pays in all years after

    it stops selling the coverage.

    (A) 75

    (B) 150

    (C) 240

    (D) 300

    (E) 360

  • 7/31/2019 May2003 ExamP

    10/40 May 2003 15 Course 1

    10. Let X and Y be continuous random variables with joint density function

    ( )

    215 for ,

    0 otherwise.

    y x y x f x y

    =

    Let g be the marginal density function of Y .

    Which of the following represents g ?

    (A) ( )15 for 0 1

    0 otherwise

    y y g y


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