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

Chapter 20
Comparing Groups
In this chapter we look at hypothesis
testing and confidence intervals used
for comparing two populations both
means and proportions.
SupposeAandBarerandomvariableswithmeansA
andBandstandarddeviationsAandB.
Thevariable(AB)hasme