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

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

17. An insurance company pays hospital claims. The number of claims that includeemergency room or operating room charges is 85% of the total number of claims.The number of claims that do not include emergency room charges is 25% of the totalnumber of claims. The occurrence of emergency room charges is independent of theoccurrence of operating room charges on hospital claims.Calculate the probability that a claim submitted to the insurance company includesoperating room charges.(A) 0.10(B) 0.20(C) 0.25(D) 0.40(E) 0.8018. Two instruments are used to measure the height, h, of a tower. The error made by theless accurate instrument is normally distributed with mean 0 and standard deviation0.0056h . The error made by the more accurate instrument is normally distributed withmean 0 and standard deviation 0.0044h .Assuming the two measurements are independent random variables, what is theprobability that their average value is within 0.005h of the height of the tower?Page 14 of 82
(A) 0.38(B) 0.47(C) 0.68(D) 0.84(E) 0.9019. An auto insurance company insures drivers of all ages. An actuary compiled thefollowing statistics on the company’s insured drivers:Age ofDriver16-2021-3031-6566-99Probabilityof Accident0.060.030.020.04Portion of Company’sInsured Drivers0.080.150.490.28A 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) 0.40Page 15 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: 16. An insurance company determines
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 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
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98. Let X 1 , X 2 , X 3 be a random
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(A) 0.47(B) 0.58(C) 0.83(D) 1.42(E)
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104. A joint density function is gi
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107. Let X denote the size of a sur
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Calculate⎡ 1⎤P⎢Y < X X =⎣ 3
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113. Two life insurance policies, e
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116. An actuary determines that the
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119. An auto insurance policy will
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⎧ 1 2⎪ ( 10 − xy ) for 2 ≤
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SOCIETY OF ACTUARIES/CASUALTY ACTUA
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4. Solution: AFor i = 1, 2, letRi=
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9. Solution: BLetM = event that cus
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14. Solution: Ak1 11 1 1 1 ⎛1⎞p
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19. Solution: BApply Bayes’ Formu
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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
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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
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105. Solution: AThe calculation req
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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
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120. Solution: AWe are given that X
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