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

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

51. A manufacturer’s annual losses follow a distribution with density function2.5⎧2.5(0.6)⎪for x > 0.63.5f( x)= ⎨ x⎪⎩ 0 otherwise.To cover its losses, the manufacturer purchases an insurance policy with an annualdeductible of 2.What is the mean of the manufacturer’s annual losses not paid by the insurance policy?(A) 0.84(B) 0.88(C) 0.93(D) 0.95(E) 1.0052. 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, theprobability of a loss of amount N is K N, for N = 1, . . . , 5 and K a constant. Theseare the only possible loss amounts and no more than one loss can occur.Determine the net premium for this policy.Page 36 of 82
(A) 0.031(B) 0.066(C) 0.072(D) 0.110(E) 0.15053. An insurance policy reimburses a loss up to a benefit limit of 10 . The policyholder’sloss, Y, follows a distribution with density function:⎧ 2⎪ for y > 13f( y)= ⎨ y⎪⎩ 0, otherwise.What is the expected value of the benefit paid under the insurance policy?(A) 1.0(B) 1.3(C) 1.8(D) 1.9(E) 2.0Page 37 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: (A) 85(B) 163(C) 168(D) 213(E) 2555
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=
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
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59. Solution: BThe distribution fun
Page 109 and 110:
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
Page 115 and 116:
( X < ) ∪ ( Y < )Pr ⎡⎣1 1 ⎤
Page 117 and 118:
40 − 3n−2≥nTo find such an n,
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-----------------------------------
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) ⎤
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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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