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

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

42. For Company A there is a 60% chance that no claim is made during the coming year.If one or more claims are made, the total claim amount is normally distributed withmean 10,000 and standard deviation 2,000 .For Company B there is a 70% chance that no claim is made during the coming year.If one or more claims are made, the total claim amount is normally distributed withmean 9,000 and standard deviation 2,000 .Assume that the total claim amounts of the two companies are independent.What is the probability that, in the coming year, Company B’s total claim amount willexceed Company A’s total claim amount?(A) 0.180(B) 0.185(C) 0.217(D) 0.223(E) 0.240Page 30 of 82
43. A company takes out an insurance policy to cover accidents that occur at itsmanufacturing plant. The probability that one or more accidents will occur duringany given month is 3 5. The number of accidents that occur in any given monthis independent of the number of accidents that occur in all other months.Calculate the probability that there will be at least four months in which no accidentsoccur before the fourth month in which at least one accident occurs.(A) 0.01(B) 0.12(C) 0.23(D) 0.29(E) 0.4144. An insurance policy pays 100 per day for up to 3 days of hospitalization and 50 per dayfor 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.Determine the expected payment for hospitalization under this policy.Page 31 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: Calculate C.(A) 0.1(B) 0.3(C) 0.4(D
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
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
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⎧ 1 2⎪ ( 10 − xy ) for 2 ≤
Page 83 and 84:
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
Page 127 and 128:
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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