Maths easy Statistics Papers

Faculty of Actuaries

Institute of Actuaries

EXAMINATION
12 April 2005 (am)

Subject CT3

Probability and Mathematical Statistics
Core Technical
Time allowed: Three hours
INSTRUCTIONS TO THE CANDIDATE

1.

Enter all the candidate and examination details as requested on the front of your answer booklet. 2.

You must not start writing your answers in the booklet until instructed to do so by the supervisor. 3.

Mark allocations are shown in brackets.

4.

Attempt all 13 questions, beginning your answer to each question on a separate sheet.

5.

Candidates should show calculations where this is appropriate.

Graph paper is required for this paper.

AT THE END OF THE EXAMINATION
Hand in BOTH your answer booklet, with any additional sheets firmly attached, and this question paper.
In addition to this paper you should have available the 2002 edition of the
Formulae and Tables and your own electronic calculator.

CT3 A2005

Faculty of Actuaries
Institute of Actuaries

1

Calculate the sample mean and standard deviation of the following claim amounts (£):
534

671

581

620

401

340

980

845

550

690
[3]

2

Suppose A, B and C are events with P ( A) = 1 , P ( B ) = 1 , P(C ) = 1 , P ( A
2
2
3
P( A

C ) = 1 , P( B
6

(a)
(b)

Determine whether or not the events A and B are independent.
Calculate the probability P( A B C ).

C) =

1
6

B) = 3 ,
4

and P ( A

B

1
C ) = 12 .

[4]

3

Claim sizes in a certain insurance situation are modelled by a distribution with moment generating function M(t) given by
M(t) = (1 10t) 2.
Show that E[X 2] = 600 and find the value of E[X 3].

4

Consider a random sample of size 16 taken from a normal distribution with mean
= 25 and variance 2 = 4. Let the sample mean be denoted X .
State the distribution of X and hence calculate the probability that X assumes a value greater than 26.

5

[3]

[3]

Consider a