Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 9
(1) An insurance company issues 5000 medical insurance policies. The number of
claims filed by a policy-holder under the insurance policy during one year has the
following probability

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 8 Solutions
(1) (Continuation of Classwork 5)
(a)
fX (x) =
Z
fX (x) =
E(X) =
0
2
x
Z
xy
x y 2 2
x3
dy = ( ) = x
2
2 2 x
4
2
x3
4
x
for 0 < x < 2
0
elsewhere
x3
x3 x5 2
= 1.0667
x (x )d

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 8
(1) (Continuation of Classwork 5)
probability density function
Let X and Y be continuous random variables with joint
f(x, y) =
xy/2
for 0 < x < y < 2
0
elsewhere
(a) Find E(X), E(Y ) a

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 11
(1) You are trying to set up a portfolio that consists of Fund X and Fund Y only. The following
information provide the joint probability distribution of X and Y in terms of the annua

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 9 Solutions
(1)
(a) Let X be the number of claims by a policyholder during one-year period.
E(X) = 0 0.75 + 1 0.12 + 2 0.08 + 3 0.05 = 0.43
E(X 2 ) = 02 0.75 + 12 0.12 + 22 0.08 + 32 0.0

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 7
(1) Given that a random sample of size 5 with y1 = 1.3, y2 = 2.4, y3 = 0.9, y4 = 2.1, y5 =
1.6 is drawn from the probability model
fY (y) =
1
22
for 1 2 < y < 1 + 2
0
elsewhere
(i) Fin

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 10 Solutions
(1) Let Yi be the random variable that policy-holder i makes a claim. Yi = 1 if he makes a
claim and Yi = 0 if he does not make a claim.
Let Xi be the random variable that t

Term 1, 16/17
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Classwork 10
(1) An insurance company provides insurance to 800 independent policy-holders with following characteristics:
For Each Insured and Given a Claim
Number
Probability of Claim
Expected
V

Term 1, 15/16
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Assignment 3
Deadline of Submission: during the class session on 8 September, 2015
1. Four motors are packaged for sale in a certain warehouse. Each motor sold generates $200
net profit. But a mon

Term 1, 15/16
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Assignment 4
Deadline of Submission: during the class session on 15 September, 2015
1.
Suppose that the cumulative distribution function of the random variable X is given
by
FX (x) =
0
for x < 1
0

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 11
No need to submit this assignment
1.
You are trying to set up a portfolio that consists of Fund X and Fund Y . Based on the
predicted economic conditions, the joint probability mass f

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 8
Deadline of Submission: during the class session on 20 October, 2015
1.
Let the joint probability density function of X and Y be
f(x, y) =
1.5y
for 0 < y < 1, y < x < 3y
0
elsewhere
(a

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 10
Deadline of Submission: during the class session on 3 November, 2015
1.
A manufacturers annual losses follow a distribution with density function:
fX (x) =
2.5(0.6)2.5
x3.5
for x > 0.

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 5
Deadline of Submission: during the class session on 22 September, 2015
1.
An urn contains four red chips, three white chips, and two blue chips. A sample of size
3 is drawn without rep

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 9
Deadline of Submission: during the class session on 27 October, 2015
1.
A random sample of size n is taken from an infinite and right-skewed population with
the mean 58 and the standar

Term 1, 15/16
STAT 201 PROBABILITY THEORY AND APPLICATIONS
Assignment 2
Deadline of Submission: During the class session on 1 September, 2015
1.
In some cases, there may have three choices of alleles. For example, 4 blood types
A, B, AB, O are determined

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 6
Deadline of Submission: during the class session on 29 September, 2015
1.
A random variable X has probability density function:
fX (x) =
2e2x
e4 1
for 0 x c
0
elsewhere
(a) Find the co

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 1
Deadline of Submission: during the class session on 25 August, 2015
1.
A class contains 12 boys and 8 girls. The teacher selects 10 of the children at random and
without replacement to

Term 1, 15/16
STAT201 PROBABILITY THEORY AND APPLICATIONS
Assignment 7
Deadline of Submission: during the class session on 13 October, 2015
1.
A random sample of size 10 with x1 = 1, x2 = 0, x3 = 1, x4 = 1, x5 = 0, x6 = 1, x7 = 1,
x8 = 1, x9 = 1 and x10 =