北美精算师(SOA)考试P 2001 November年真题
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
November 2001 Course 1
Mathematical Foundations of Actuarial Science
Society of Actuaries/Casualty Actuarial Society
1.
An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 .
S = 175 L 3/2 A 4/5.
Which of the following statements is true?
(A) (B) (C) (D) (E)
S increases at an increasing rate as L increases and increases at a decreasing rate as A increases. S increases at an increasing rate as L increases and increases at an increasing rate as A increases. S increases at a decreasing rate as L increases and increases at a decreasing rate as A increases. S increases at a decreasing rate as L increases and increases at an increasing rate as A increases. S increases at a constant rate as L increases and increases at a constant rate as A increases.
∫∫
R
f(x, y) dA = 6 .
Determine
∫∫
R
[4f(x, y) – 2] dA .
(A) (B) (C) (D) (E)
12 18 20 22 44
Course 1, November 2001
3
3.
Sales, S, of a new insurance product are dependent upon the labor, L, of the sales force and the amount of advertising, A, for the product. The relationship can be modeled by
(A) (B) (C) (D) (E)
0.031 0.066 0.072 0.110 0.150
Course 1, November 2001
6
6.
Let C be the curve defined by the parametric equations x = t2 + t, y = t2 – 1 .
Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival?
(A) (B) (C) (D) (E)
0.06 0.29 0.30 0.39 0.64
Let C1 = X+Y denote the size of the combined claims before the application of a 20% surcharge on the hospital portion of the claim, and let C2 denote the size of the combined claims after the application of that surcharge.
Calculate Cov(C1, C2).
(A) (B) (C) (D) (E)
8.80 9.60 9.76 11.52 12.32
Course 1, November 2001
8
8.
A medical researcher conducts a ten-week study of patients infected with a chronic disease. Over the course of the study, the researcher finds that the fraction of patients exhibiting severe symptoms can be modeled as
Determine the probability that a randomly chosen member of this group visits a physical therapist.
(A) (B) (C) (D) (E)
0.26 0.38 0.40 0.48 0.62
Course 1, November 2001
7
7.
Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which E(X) = 5, E(X 2) = 27.4, E(Y) = 7, E(Y 2) = 51.4, and Var(X+Y) = 8 .
F ( t ) = te − t
where t is time elapsed, in weeks, since the study began.
What is the minimum fraction of patients exhibiting severe symptoms between the end of the first week and the end of the seventh week of the study?
10
10.
Let {an} be a sequence of real numbers.
For which of the following does the infinite series
1 a + converge? ∑ n
n n =1
∞
(A) (B) (C) (D) (E)
an = 1 an = 1 n an = 12 n an =
K , for N = 1, . . . , 5 and K a constant. These N
are the only possible loss amounts and no more than one loss can occur.
Determine the net premium for this policy.
3 . The number of accidents that occur in any given month 5
is 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 accidents occur before the fourth month in which at least one accident occurs.
(A) (B) (C) (D) (E)
0.01 0.12 0.23 0.29 0.41
Course 1, November 2001
12
12.
Let f be a function such that f ′(0) = 0 . The graph of the second derivative f ′′ is shown below.
Calculate the number of blue balls in the second urn.
(A) (B) (C) (D) (E)
4 20 24 44 64
Course 1, Noቤተ መጻሕፍቲ ባይዱember 2001
2
2.
Let R be a region in the xy-plane with area 2 . Let
(A) (B) (C) (D) (E)
0.0000 0.0004 0.0027 0.0064 0.3679
Course 1, November 2001
9
9.
Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist.
Course 1, November 2001
5
5.
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, the probability of a loss of amount N is
Course 1, November 2001
4
4.
Upon arrival at a hospital’s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year: (i) (ii) (iii) (iv) (vi) (vii) 10% of the emergency room patients were critical; 30% of the emergency room patients were serious; the rest of the emergency room patients were stable; 40% of the critical patients died; 10% of the serious patients died; and 1% of the stable patients died.
Determine the value of t at which the line tangent to the graph of C is parallel to the line 5y – 4x = 3 .
(A)
−
1 10 2 5 5 8 5 3
(B)
(C)
(D) (E)
2
Course 1, November 2001
(–1)n n
− an = 1 2n n
Course 1, November 2001
11
11.
A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is
Mathematical Foundations of Actuarial Science
Society of Actuaries/Casualty Actuarial Society
1.
An urn contains 10 balls: 4 red and 6 blue. A second urn contains 16 red balls and an unknown number of blue balls. A single ball is drawn from each urn. The probability that both balls are the same color is 0.44 .
S = 175 L 3/2 A 4/5.
Which of the following statements is true?
(A) (B) (C) (D) (E)
S increases at an increasing rate as L increases and increases at a decreasing rate as A increases. S increases at an increasing rate as L increases and increases at an increasing rate as A increases. S increases at a decreasing rate as L increases and increases at a decreasing rate as A increases. S increases at a decreasing rate as L increases and increases at an increasing rate as A increases. S increases at a constant rate as L increases and increases at a constant rate as A increases.
∫∫
R
f(x, y) dA = 6 .
Determine
∫∫
R
[4f(x, y) – 2] dA .
(A) (B) (C) (D) (E)
12 18 20 22 44
Course 1, November 2001
3
3.
Sales, S, of a new insurance product are dependent upon the labor, L, of the sales force and the amount of advertising, A, for the product. The relationship can be modeled by
(A) (B) (C) (D) (E)
0.031 0.066 0.072 0.110 0.150
Course 1, November 2001
6
6.
Let C be the curve defined by the parametric equations x = t2 + t, y = t2 – 1 .
Given that a patient survived, what is the probability that the patient was categorized as serious upon arrival?
(A) (B) (C) (D) (E)
0.06 0.29 0.30 0.39 0.64
Let C1 = X+Y denote the size of the combined claims before the application of a 20% surcharge on the hospital portion of the claim, and let C2 denote the size of the combined claims after the application of that surcharge.
Calculate Cov(C1, C2).
(A) (B) (C) (D) (E)
8.80 9.60 9.76 11.52 12.32
Course 1, November 2001
8
8.
A medical researcher conducts a ten-week study of patients infected with a chronic disease. Over the course of the study, the researcher finds that the fraction of patients exhibiting severe symptoms can be modeled as
Determine the probability that a randomly chosen member of this group visits a physical therapist.
(A) (B) (C) (D) (E)
0.26 0.38 0.40 0.48 0.62
Course 1, November 2001
7
7.
Let X denote the size of a surgical claim and let Y denote the size of the associated hospital claim. An actuary is using a model in which E(X) = 5, E(X 2) = 27.4, E(Y) = 7, E(Y 2) = 51.4, and Var(X+Y) = 8 .
F ( t ) = te − t
where t is time elapsed, in weeks, since the study began.
What is the minimum fraction of patients exhibiting severe symptoms between the end of the first week and the end of the seventh week of the study?
10
10.
Let {an} be a sequence of real numbers.
For which of the following does the infinite series
1 a + converge? ∑ n
n n =1
∞
(A) (B) (C) (D) (E)
an = 1 an = 1 n an = 12 n an =
K , for N = 1, . . . , 5 and K a constant. These N
are the only possible loss amounts and no more than one loss can occur.
Determine the net premium for this policy.
3 . The number of accidents that occur in any given month 5
is 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 accidents occur before the fourth month in which at least one accident occurs.
(A) (B) (C) (D) (E)
0.01 0.12 0.23 0.29 0.41
Course 1, November 2001
12
12.
Let f be a function such that f ′(0) = 0 . The graph of the second derivative f ′′ is shown below.
Calculate the number of blue balls in the second urn.
(A) (B) (C) (D) (E)
4 20 24 44 64
Course 1, Noቤተ መጻሕፍቲ ባይዱember 2001
2
2.
Let R be a region in the xy-plane with area 2 . Let
(A) (B) (C) (D) (E)
0.0000 0.0004 0.0027 0.0064 0.3679
Course 1, November 2001
9
9.
Among a large group of patients recovering from shoulder injuries, it is found that 22% visit both a physical therapist and a chiropractor, whereas 12% visit neither of these. The probability that a patient visits a chiropractor exceeds by 0.14 the probability that a patient visits a physical therapist.
Course 1, November 2001
5
5.
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, the probability of a loss of amount N is
Course 1, November 2001
4
4.
Upon arrival at a hospital’s emergency room, patients are categorized according to their condition as critical, serious, or stable. In the past year: (i) (ii) (iii) (iv) (vi) (vii) 10% of the emergency room patients were critical; 30% of the emergency room patients were serious; the rest of the emergency room patients were stable; 40% of the critical patients died; 10% of the serious patients died; and 1% of the stable patients died.
Determine the value of t at which the line tangent to the graph of C is parallel to the line 5y – 4x = 3 .
(A)
−
1 10 2 5 5 8 5 3
(B)
(C)
(D) (E)
2
Course 1, November 2001
(–1)n n
− an = 1 2n n
Course 1, November 2001
11
11.
A company takes out an insurance policy to cover accidents that occur at its manufacturing plant. The probability that one or more accidents will occur during any given month is