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

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

70. An insurance company sells an auto insurance policy that covers losses incurred by apolicyholder, subject to a deductible of 100 . Losses incurred follow an exponentialdistribution with mean 300.What is the 95 th percentile of actual losses that exceed the deductible?(A) 600(B) 700(C) 800(D) 900(E) 100071. The time, T, that a manufacturing system is out of operation has cumulative distributionfunction2⎧ ⎛2⎞⎪1− for t > 2Ft () = ⎜ ⎟⎨ ⎝ t ⎠⎪⎩0 otherwise.The resulting cost to the company isY2= T .Determine the density function of Y, for y > 4 .Page 48 of 82
4(A)2y8(B)3/2y8(C)3y(D)16y1024(E)5y72. An investment account earns an annual interest rate R that follows a uniform distributionon the interval ( 0.04, 0.08 ). The value of a 10,000 initial investment in this account afterone year is given by V= 10,000eR .Determine the cumulative distribution function, F( v ) , of V for values of v that satisfy( )0< F v < 1.(A)(B)(C)(D)v/10,00010,000e−10,408425v/10,00025e − 0.04v −10,40810,833−10,40825v⎡ ⎛ v ⎞ ⎤(E) 25 ⎢ln ⎜ − 0.04⎥10,000⎟⎣ ⎝ ⎠ ⎦Page 49 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 and 34: 46. A device that continuously meas
Page 35 and 36: (A) 85(B) 163(C) 168(D) 213(E) 2555
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: (A) 161(B) 165(C) 173(D) 182(E) 250
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=
Page 87 and 88: 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
Page 95 and 96: 31. Solution: DLet X denote the num
Page 97 and 98: 36. Solution: BTo determine k, note
Page 99 and 100:
41. Solution: ELetX = number of gro
Page 101 and 102:
44. Solution: CIf k is the number o
Page 103 and 104:
5( ) ⎤ = ∑ ( ) Pr[ = ]E⎡⎣f
Page 105 and 106:
54. Solution: BLet Y denote the cla
Page 107 and 108:
59. Solution: BThe distribution fun
Page 109 and 110:
64. Solution: ALet X denote claim s
Page 111 and 112:
68. Solution: CNote that X has an e
Page 113 and 114:
74. Solution: EFirst note R = 10/T
Page 115 and 116:
( X < ) ∪ ( Y < )Pr ⎡⎣1 1 ⎤
Page 117 and 118:
40 − 3n−2≥nTo find such an n,
Page 119 and 120:
-----------------------------------
Page 121 and 122:
92. Solution: BLet X and Y denote t
Page 123 and 124:
⎧ 1⎪ , 0< t1 < 6 , 0< t2 < 6 ,
Page 125 and 126:
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) ⎤
Page 131 and 132:
111. Solution: E3 f ( 2, y)Pr ⎡
Page 133 and 134:
116. Solution: DDenote the number o
Page 135 and 136:
120. Solution: AWe are given that X
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