P_PracticeExam6_05-1..
P_PracticeExam6_05-1..
P_PracticeExam6_05-1..
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PRACTICE EXAMINATION NO. 6<br />
17. The time to failure X of an MP3 player follows a Weibull distribution. It is known that<br />
Pr( X > 3)<br />
= 1<br />
1<br />
, and that Pr( X > 6)<br />
= . Find the probability that this MP3 player is still<br />
4<br />
e e<br />
functional after 4 years.<br />
A. 0.0498 B. 0.0821 C. 0.1353 D. 0.1690 E. 0.2231<br />
18. You are given that the hazard rate for a random variable X is<br />
! X ( x)<br />
= 1<br />
x" 1<br />
2<br />
2<br />
for x > 0, and zero otherwise. Find the mean of X.<br />
A. 1 B. 2 C. 2.5 D. 3 E. 3.5<br />
19. Let P be the probability that an MP3 player produced in a certain factory is defective, with P<br />
assumed a priori to have the uniform distribution on [0, 1]. In a sample of one hundred MP3<br />
players, 1 is found to be defective. Based on this experience, determine the posterior expected<br />
value of P.<br />
A. 1<br />
100<br />
2<br />
B.<br />
101<br />
20. You are given that Pr A<br />
Pr C A ! B<br />
A. 1<br />
3<br />
( ) = 1<br />
2<br />
2<br />
B.<br />
5<br />
2<br />
C.<br />
99<br />
( ) = 2<br />
. Find Pr( A B ! C).<br />
1<br />
D.<br />
50<br />
1<br />
E.<br />
51<br />
3<br />
1<br />
1<br />
, Pr( A ! B)<br />
= , Pr( B A)<br />
= , Pr( C B)<br />
= , and<br />
5 5 4 3<br />
3<br />
C.<br />
10<br />
1<br />
D.<br />
2<br />
1<br />
E.<br />
4<br />
2<strong>1.</strong> Let X( 1)<br />
,..., X( n)<br />
be the order statistics from the uniform distribution on [0, 1]. Find the<br />
correlation coefficient of X( 1)<br />
and X( n)<br />
.<br />
A. ! 1<br />
n<br />
B. ! 1<br />
n + 1<br />
C. 0 D. 1<br />
n + 1<br />
E. 1<br />
n<br />
ASM Study Manual for Course P/1 Actuarial Examination. © Copyright 2004-2007 by Krzysztof Ostaszewski - 255 -
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