Name:
ID:
1.
A random variable X is assumed to satisfy X(
Θ
=
) ~ Pareto (
, β = 1200), and thus
Ɵ
Ɵ
= , x > 0
and the prior distribution for
is Exponential with mean 5, i.e.
Ɵ
,
>0.
Ɵ
Determine the
posterior distribution
of
given X = 155 (i.e. say which type of distribution it is and what are
the parameters).
2.
Suppose that given
the random variables X
1
, …, X
n
are i.i.d. with pf
(x
j
)=
(belongs to LEF)
Where
has pdf
()=
Determine the parameters in the resulting posterior distribution.
3.
Claim sizes follow the distribution (density function)
,
are unknown. The following sample of claim sizes is available:
12, 25, 35, 40, 70, 150,
250. Percentile matching at the 50
th
percentile is used to estimate.
Determine the resulting estimate of
4.
Two hundred losses are observed. Three of the losses are 300, 500, 800. All that is known
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 Fall '09
 davidlandriault
 Normal Distribution, Probability theory, posterior distribution, random variables X1, ɵ

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