20052009年英国精算师考试ct3 历年真题及答案解析.pdf

Faculty of Actuaries Institute of Actuaries
EXAMINATION
April 2005
Subject CT3 Probability and Mathematical Statistics
Core Technical
EXAMINERS REPORT
Introduction
The attached subject report has been written by the Principal Examiner with
the aim of helping candidates. The questions and comments are based around
Core Reading as the interpretation of the syllabus to which the examiners are
working. They have however given credit for any alternative approach or
interpretation which they consider to be reasonable.
M Flaherty
Chairman of the Board of Examiners
15 June 2005
Faculty of Actuaries
Institute of Actuaries
Subject CT3 (Probability and Mathematical Statistics Core Technical) April 2005 Examiners Report
1 x = 6212 , x2 = 4186784
6212
x = £
10
1 62122
s 4186784 = £
9 10 9
1 1 3 1
2 (a) P(A B) P(A) P(B) P(A B) 2 2 4 4
1 1 1
P(A)P(B) ( 2)( 2) 4 so the events A and B are independent as
P(A B) P(A)P(B).
(b) P(A B C) P(A) P(B) P(C) P(A B) P(A C) P(B C)
P(A B C)
1 1 1 1 1 1 1 5
2 2 3 4 6 6 12 6
[OR P(A B C) P(A B) P(C) P(A C) P(B C) P(A B C)
3 1 1 1 1 5
4 3 6 6 12 6 .]