SOA/CAS Exam P Sample Questions - The Online Test Page

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$Name: Quiz 5 Math 100 Fall 2011 1. (10 pts.) Consider the equation ...$

48. An insurance policy on an electrical device pays a benefit of 4000 if the device failsduring the first year. The amount of the benefit decreases by 1000 each successive yearuntil it reaches 0 . If the device has not failed by the beginning of any given year, theprobability of failure during that year is 0.4 .What is the expected benefit under this policy?(A) 2234(B) 2400(C) 2500(D) 2667(E) 269449. An insurance policy pays an individual 100 per day for up to 3 days of hospitalizationand 25 per day for each day of hospitalization thereafter.The number of days of hospitalization, X, is a discrete random variable with probabilityfunction⎧6− k⎪ for k = 1, 2,3, 4,5PX ( = k) =⎨ 15⎪⎩ 0 otherwise.Calculate the expected payment for hospitalization under this policy.Page 34 of 82
(A) 85(B) 163(C) 168(D) 213(E) 25550. A company buys a policy to insure its revenue in the event of major snowstorms that shutdown business. The policy pays nothing for the first such snowstorm of the year and10,000 for each one thereafter, until the end of the year. The number of majorsnowstorms per year that shut down business is assumed to have a Poisson distributionwith mean 1.5 .What is the expected amount paid to the company under this policy during a one-yearperiod?(A) 2,769(B) 5,000(C) 7,231(D) 8,347(E) 10,578Page 35 of 82
Page 1 and 2: SOCIETY OF ACTUARIES/CASUALTY ACTUA
Page 3 and 4: 2. The probability that a visit to
Page 5 and 6: (A) 280(B) 423(C) 486(D) 880(E) 896
Page 7 and 8: 8. Among a large group of patients
Page 9 and 10: 11. An actuary studying the insuran
Page 11 and 12: What is the probability that a woma
Page 13 and 14: 16. An insurance company determines
Page 15 and 16: (A) 0.38(B) 0.47(C) 0.68(D) 0.84(E)
Page 17 and 18: 21. Upon arrival at a hospital’s
Page 19 and 20: 24. The number of injury claims per
Page 21 and 22: 27. A study of automobile accidents
Page 23 and 24: 30. An actuary has discovered that
Page 25 and 26: 33. The loss due to a fire in a com
Page 27 and 28: 37. The lifetime of a printer costi
Page 29 and 30: Calculate C.(A) 0.1(B) 0.3(C) 0.4(D
Page 31 and 32: 43. A company takes out an insuranc
Page 33: 46. A device that continuously meas
Page 37 and 38: (A) 0.031(B) 0.066(C) 0.072(D) 0.11
Page 39 and 40: 56. An insurance policy is written
Page 41 and 42: 59. An insurer's annual weather-rel
Page 43 and 44: 63. The warranty on a machine speci
Page 45 and 46: 66. A company agrees to accept the
Page 47 and 48: (A) 161(B) 165(C) 173(D) 182(E) 250
Page 49 and 50: 4(A)2y8(B)3/2y8(C)3y(D)16y1024(E)5y
Page 51 and 52: (D)(E)102r52 2 r75. The monthly pro
Page 53 and 54: 78. A device runs until either of t
Page 55 and 56: 82. An insurance company issues 125
Page 57 and 58: 85. The total claim amount for a he
Page 59 and 60: 88. The waiting time for the first
Page 61 and 62: 91. An insurance company insures a
Page 63 and 64: 95. X and Y are independent random
Page 65 and 66: 98. Let X 1 , X 2 , X 3 be a random
Page 67 and 68: (A) 0.47(B) 0.58(C) 0.83(D) 1.42(E)
Page 69 and 70: 104. A joint density function is gi
Page 71 and 72: 107. Let X denote the size of a sur
Page 73 and 74: Calculate⎡ 1⎤P⎢Y < X X =⎣ 3
Page 75 and 76: 113. Two life insurance policies, e
Page 77 and 78: 116. An actuary determines that the
Page 79 and 80: 119. An auto insurance policy will
Page 81 and 82: ⎧ 1 2⎪ ( 10 − xy ) for 2 ≤
Page 83 and 84: SOCIETY OF ACTUARIES/CASUALTY ACTUA
Page 85 and 86:
4. Solution: AFor i = 1, 2, letRi=
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9. Solution: BLetM = event that cus
Page 89 and 90:
14. Solution: Ak1 11 1 1 1 ⎛1⎞p
Page 91 and 92:
19. Solution: BApply Bayes’ Formu
Page 93 and 94:
25. Solution: BLet Y = positive tes
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31. Solution: DLet X denote the num
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36. Solution: BTo determine k, note
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41. Solution: ELetX = number of gro
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44. Solution: CIf k is the number o
Page 103 and 104:
5( ) ⎤ = ∑ ( ) Pr[ = ]E⎡⎣f
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54. Solution: BLet Y denote the cla
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59. Solution: BThe distribution fun
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64. Solution: ALet X denote claim s
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68. Solution: CNote that X has an e
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74. Solution: EFirst note R = 10/T
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( X < ) ∪ ( Y < )Pr ⎡⎣1 1 ⎤
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40 − 3n−2≥nTo find such an n,
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-----------------------------------
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92. Solution: BLet X and Y denote t
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⎧ 1⎪ , 0< t1 < 6 , 0< t2 < 6 ,
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99. Solution: C2We use the relation
Page 127 and 128:
105. Solution: AThe calculation req
Page 129 and 130:
228= Var[ X + Y] = E⎡( X + Y) ⎤
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111. Solution: E3 f ( 2, y)Pr ⎡
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116. Solution: DDenote the number o
Page 135 and 136:
120. Solution: AWe are given that X
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