Chapter 2: Probability
2.1
Set Theory
Experiment
Definition: Experiment is a process that generates a set of data.
Examples of experiment are the tossing of a coin and tossing of a dice.
Sample Space
Definition: Sample space is a set of all possible outco

Chapter 4: Expectation
Expectation
The expected value of a random variable is an average value (mean).
For example, a student tosses two coins 12 times. The student wants to know his
average or expected number of heads per toss. X is the number of heads t

Chapter 4: Expectation
Expectation
The expected value of a random variable is an average value (mean).
For example, a student tosses two coins 12 times. The student wants to know his
average or expected number of heads per toss. X is the number of heads t

QMT200
Tutorial 4
1.
A random variable X has the probability density function as in the following table.
x
-2
3
1
1/3
1/2
1/6
f (x)
a. Find E (X ) and E (4 X 1)
b. Find Var (X ) and Var (3 X 2)
c. Find the moment generating function of X .
2.
Suppose that

Tutorial 2
1. A family has 2 children. Find the probability that all the children are girls.
2. A die is rolled twice, find the sample space. Compute the probability of getting both
numbers less than four.
3. Consider a die-toss experiment. Define the fol

QMT 200
Probability and Statistics 1
Nurdia Azlin Ghazali
Faculty of Computer and Mathematical Sciences
Universiti Teknologi Mara Johor
QMT 200
Chapter 1: Methods of Counting
1.1
Permutation
A permutation is an arrangement of all or part of a set of objec

Tutorial 7
1. Let X and Y be discrete random variables having joint density function
a. Find the marginal density function of X and Y.
b. Find P(X = 2, Y = 3)
c. Find P(1 X 2, Y 2)
d. Find P(X 2)
e. Find P(Y < 2)
f.
Determine whether X and Y are independe

Tutorial 5: Answer
5.2
P(X=3) =0.0537
5.5
a)
b)
5.6
X= no of companies
p=0.5 , n=6
a)
b)
5.9
p=0.75(have blowout), n=15, X no of trucks
a)
0.0042
b)
5.11
p=0.9, n=7, X= no of patients
5.12
p=0.25, n=9, X= no of vehicles passing through a cehckpoint are fr

Chapter 5: Special Discrete Probability Distribution
5.1
Binomial Distribution
Binomial Experiment
An experiment which consists of n independent trials, whose outcome of each trial is
either a success with probability p or a failure with probability 1- p.

CONFIDENTIAL
CS/APR 2010/QMT200/400
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
COURSE CODE
PROBABILITY AND STATISTICS I /
PROBABLITY AND STATISTICS
QMT200/400
EXAMINATION
APRIL 2010
TIME
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper co

Centre of Studies for Quantity Surveying
Faculty of Architecture, Planning & Surveying
Universiti Teknologi MARA
Shah Alam, Selangor
FINAL PROJECT/DISSERTATION
QSM 664/QSB 674
PROGRAMME
SEMESTER
PART
NAME
MATRIC/UITM NO.
ADDRESS
CONTACT NO.
: BACHELOR OF

Engineering and Construction Joint Ventures: Patterns and Findings from Current
Research
Daniel Dushie
IDP Ghana 2011, Andrews University, Berrien Springs, USA.
Procurement and Project Management Consultancy
# 13 Jungle Road, East Legon. P.O.Box AF 1701,

CONTENT
DECLARATION
ABSTRACT
ACKNOWLEDGEMENT
TABLE OF CONTENTS
LIST OF FIGURE
LIST OF TABLE
LIST OF ABBREVIATION
CHAPTER 1: INTRODUCTION
1.1 Background of Research
1.2 Problem Statement
1.3 Aim
1.4 Objective
1.5 Scope and Limitation
1.5.1 Scope
1.5.2 Limi

INNOVATIVE ENTREPRENEURIAL GLOBAL
Probability
1
Prepared by Razana Alwee / Updated by Nor Erne Nazira & Shukor Talib
Probability
Should you buy an extended warranty for a new smart phone?
Should you allow 45 minutes to get to your 8.00 A.M class or
35 is

INNOVATIVE ENTREPRENEURIAL GLOBAL
Descriptive Statistics
Measures of Central Tendency
1
Prepared by Razana Alwee / Updated by Suhaila Mohamad Yusuf
Measures of Central Tendency
A measure of central tendency of a distribution is a
numerical value that desc

INNOVATIVE ENTREPRENEURIAL GLOBAL
Presenting Qualitative Data
1
Prepared by Razana Alwee / Updated by Suhaila Mohamad Yusuf
Categorical Data (Qualitative Data)
An appropriate graphical or tabular of data can be an
effective way to summarize and communicat

Chapter 5: Special Discrete Probability Distribution
5.1 Binomial Distribution
Binomial Experiment
An experiment which consists of n independent trials, whose outcome of each trial is
either a success with probability p or a failure with probability 1- p.

QMT200
Tutorial 3
1. The probability density function of a continuous random variable X is given as
xe x ,
x0
f ( x)
0 , elsewhere
a. Find the cumulative distribution of X
b. Find P( X 2)
c. Find P( X 4)
(October 2009, Q2)
2. The number of emergency ca

Chapter 3: Probability Distribution and Probability Densities
3.1
Random Variables
Random Experiment
An experiment which is the outcome cannot be predicted with certainty.
Random Variable
A function, that assigns a real number to each element in the sampl

Example 8
The probability of regular scheduled flight departs on time is 0.83; the probability that it
arrives on time is 0.85 and the probability that it departs and arrives on time is 0.78. Find the
probability that a plane
a) Arrives on time given it d

CONFIDENTIAL
CS/APR 2007/QMT200
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
:
PROBABILITY AND STATISTICS 1
COURSE CODE
:
QMT200
EXAMINATION
:
APRIL 2007
TIME
:
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper consists of ten (10) questions

CS/APR 2008/QMT200
CONFIDENTIAL
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
:
PROBABILITY AND STATISTICS 1
COURSE CODE
:
QMT200
EXAMINATION
:
APRIL 2008
TIME
:
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper consists of ten (10) questions

CONFIDENTIAL
CS/APR 2009/QMT200/400
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
PROBABILITY AND STATISTICS 1 / PROBABILITY
COURSE CODE
QMT200/400
EXAMINATION
APRIL 2009
TIME
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper consists of ten

CONFIDENTIAL
CS/APR 2006/QMT200
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
PROBABILITY AND STATISTICS 1
COURSE CODE
QMT200
EXAMINATION
APRIL 2006
TIME
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper consists of ten (10) questions.
2.
Ans

Chapter 2: Probability
2.1
Set Theory
Experiment
Definition: Experiment is a process that generates a set of data.
Examples of experiment are the tossing of a coin and tossing of a die.
Sample Space
Definition: Sample space is a set of all possible outcom

Chapter 6: Special Continuous Probability Distribution
6.1
The Uniform Distribution
Definition
A random variable X is uniformly distributed on the interval (a, b) with probability
density function is given by
1
, a x b
f ( x) b a
0,
elsewhere
Probabilit

CONFIDENTIAL
CS/APR 2011 /QMT200/400/STA150/400
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
PROBABILITY AND STATISTICS 1/ PROBABILITY
AND STATISTICS
COURSE CODE
QMT200/400/STA150/400
EXAMINATION
APRIL 2011
TIME
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.

CS/OCT 2007/QMT200
CONFIDENTIAL
UNIVERSITI TEKNOLOGI MARA
FINAL EXAMINATION
COURSE
:
PROBABILITY AND STATISTICS 1
COURSE CODE
:
QMT200
EXAMINATION
:
OCTOBER 2007
TIME
:
3 HOURS
INSTRUCTIONS TO CANDIDATES
1.
This question paper consists of ten (10) questio

Chapter 7: Functions of Random Variables
7.1
2 Dimensional discrete random variables
Definition: Let X and Y be two discrete random variables. A function f(x,y) is called the
joint probability density function of the random variable (X, Y) if the followin