Question 26 you are given 1 the prior distribution

Question 26
You are given:
(1) The prior distribution for the parameter O is inverse exponential with parameter 2.
(ii) Given 0 = B , claim sizes follow a gamma distribution with parameters
a
= 2 and B
Claim amounts 1 and 2 are observed for the first two claims.
Which of the following is the posterior distribution of 0 ?
.
A Gamma with parameters a= 6, 8=
Gamma with parameters a= 5, B =
Inverse gamma with parameters
a =
5, 8
=
Inverse gamma with parameters
a =
6, B
=
5
B 5
C 5
D 5
Exam C Questions - Chapter 9
E Single parameter Pareto with a = 5,0 = 2
BPP Professional Education: Summer/Fall 2012 Page 13

Question 27
You are given:
( 1 )
The number of claims is
Poisson(.)
(ii) The prior distribution for 2 is a gamma(2,0.20) distribution
(iii)A random sample of claims numbers gives the values:
0 0 1 0 1 0 2 2 0 0
Determine the Bayesian estimate for 2 assuming a squared-error loss function.
B
C
D
E
Questions - Chapter 9 Exam C
Question 28
You are given:
(i) Claim numbers have a Poisson(,) distribution
(ii) The following prior distribution is to be
used for
2: TI - (2)=
0.6
[5e - 52 ]+
0.4 [1002e -102
2 >
(iii)During the last year, two claims were received. Determine the
Bayesian estimate for
2
assuming a squared-error loss function.
],
0
B 0.46
C 0.47
D 0.48
E 0.49
Page 14 © BPP Professional Education: Summer/Fall 2012

Question 29
You are given the following information about 4 dice:
Dice Probability of throwing a six
1-2 1/6
3 1/2
4 1/10
A dice is chosen at random, and the following sequence of results is obtained, where "1" indicates
that a six is thrown, and "0" indicates that a six is not thrown:
{X
i
, X
2
,
X
3
} = {
0,0,1}
Determine the expected value of
X4 I
S , where
X4 is
the next result for the same dice.
Question 30
You are given:
Policies in a portfolio can produce either 0,1 or 2 claims in a year.
For each policy, the number of claims in a year has the distribution:
Number of claims 0 1 2
Probability 2q 0.6-g 0.4 -
( i i i ) T h e pr i o r d en s i ty fo r q i s :
A
-
(q)= 156.25q
3
,
0 q
(iv) A policy from the portfolio produced one claim last year.
Determine the Bayesian estimate of the number of claims next year from the same policy.
g
.4
A between 0.40 and 0.45
between 0.45 and 0.50
between 0.50 and .55
between 0.55 and 0.60
B
C
D