Faculty of Actuaries Institute of Actuaries
EXAMINATIONS
Subject C — Statistics
Paper One
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE
1. Write your surname in full, the initials of your other names and your
Candidate’s Number on the front of the answer booklet.
2. Begin your answers to Parts One, Two and Three on a separate sheet.
3. Mark allocations are shown in brackets.
4. Attempt all 16 questions.
Graph paper is required for this paper.
AT THE END OF THE EXAMINATION
Hand in BOTH your answer booklet and this question paper.
In addition to this paper you should have available graph paper,
Actuarial Tables and an electronic calculator.
ã Faculty of Actuaries
C1—A99 ã Institute of Actuaries
C1(A)—2
PART ONE
For questions 1–7 indicate in your answer booklet which one of the answers A, B, C or D
is correct.
1 A workman charges his customers at the rate of £30 per hour, plus a call-out
charge of £40. Over a particular week the mean and standard deviation of the
lengths of his jobs are 5hr and 0.5hr respectively.
The mean and standard deviation of the costs (£) incurred by his customers
that week are respectively
A 190 and 15
B 190 and 55
C 150 and 7.5
D 150 and 15 [2]
2 In a large collection of life policies, 60% are for male lives, and 15% of the
sums assured on these lives exceed £200,000. The percentage of sums assured
on female lives which exceed £200,000 is 6%.
A policy is selected from this collection at random. The sum assured on the life
concerned is £145,000.
The probability that the selected policy is for a female life is:
A 0.376
B 0.424
C 0.510
D 0.576 [3]
3 For each of a number of independent inquiries at an insurance firm’s inquiry
desk the probability that it leads to a sale is 0.6. N, the number of inquiries
made until the 3rd sale is made, is recorded on a particular day.
The probability that N = 8 is
A 0.0464
B 0.1045
C 0.1239
D 0.2787 [3]
C1(A)—3 PLEASE TURN OVER
4 A simple discrete random variable, X, has probability function given by
P(X = 0) = 0.4
P(X = 1) = 0.6.
The coefficient of skewness is:
A -0.048
B -0.098
C -0.20
D -0.41 [3]
5 Suppose that claim sizes of a certain type can be modelled by a normal random
variable with mean m = £500 and standard deviation s = £100.
The moment generating function of the difference between two independent
claim sizes (£), M(t), is given by:
A M(t) = exp(10,000t2)
B M(t) = exp(1000 + 10,000t2)
C M(t) = exp(1000t + 10,000t2)
D M(t) = exp(1000t) [3]
6 Let X and Y have joint density function given by
f (x, y) = 2 ( x + y) : < x < , < y < .
3
2 0 1 0 1
The conditional density function of X given Y = y is
A
2
1
0
x y
y
x y
+
+
: < <
B
2
1
0 1
x y
y
x
+
+
: < <
C
2
2
0
x y
y
x y
+
+
: < <
D
2
2
0 1
x y
y
x
+
+
: < < [3]
C1(A)—4
7 It is desired to simulate an observation of the random variable X with
probability density function
f x k
b g = x k
£ £ RS |
T|
1
0
0
;
otherwise
A random number r is generated from the uniform distribution over [0, 1]. The
following values are then calculated
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