Midterm 1 STT459 SOLUTION NAME
In the following problems X is a random variable with pdf ( )
()
Problem 1. What is the survival function
(1)
(2)
(3)
.
?
(4)
Problem 2. What is the coefficient of variation?
(1)
(2)
(3)
(4)
()
?
Problem 4. What is the mean
STT459- Quiz 1
SOLUTION
Let X be a positive random variable with density ( )
a.
Find the hazard rate function ( )
(
)
Find the mean excess loss function ( )
(
)
d.
(1).
)
c.
(1).
(
b.
(1).
Find the survival function ( )
Find
(1).
e.
(1).
(2)
(
(2)
(2)
(
STT459- Quiz 2 SOLUTION
Name:
Let X be a positive random variable with density ( )
(
, where
)
parameter.
a.
Let
(1).
b.
(
(2)
)
Find
(1).
c.
, where c>0. Find the density of
(
(
(
(3)
)
(
)
)
(4)
(
(
)
)
(2)
(
(
(1).
(2)
(
(
(
)
)
(3)
(
(
)
)
(4)
). Reca
STT459- Quiz 3 SOLUTION
Name:
The following relates to the first 3 problems. Let X be a positive random variable that denotes the loss
in the current year. Assume that X is distributed lognormal with
.
(
Remark.
1.
)
()
(
)
(
()
(
)
What is the average lo
STT459- Quiz 4 SOLUTION Name:
A compound Poisson random variable has the representation:
independent,
are identically distributed and
1) Assume X is discrete with
(1) .013 (2) .23 (3) .18
.
and
, where
are
Find P(S=2)
(4) .13
Answer: (4).
The following re
STT459- Quiz 4
The loss
SOLUTION
Name:
has an exponential distribution with mean
Recall that if
exponential with mean
(
then:
1. In what follows use deductible
)
.
Also, for any positive random variable
(
)
(
)
Find the following
1)
2)
3)
()
(1) .05
(2) .