STAT220
EngineeringStatistics
Unit3:
DiscreteRandomVariables
RandomVariables
p
p
A randomvariable isavariablethatassignsanumerical
value to each outcome of a random experiment or trial
(denotedbyuppercaseletters).
A discrete randomvariableisar.v.withafini
STAT220
EngineeringStatistics
Unit2:
Probability
Sample Spaces and Events
RandomExperiments:
Anexperimentthatcanresultindifferentoutcomes,eventhough
it is repeated in the same manner everytime,is called random
experiment.
Outcome: An outcome is defined as
STAT220
EngineeringStatistics
Unit10:
AnalysisofVariance
ExperimentalDesign
Up until now, we have considered only two ways of
collectingandcomparingdata:
Usingindependentrandomsamples
Usingpaired(ormatched)samples
Oftendataiscollectedastheresultofanexperi
TwoWayAnalysisofVariance
A twofactorfactorialdesign comparesthemeanresponse
for a levels offactor Aandeach of b levelsoffactorB.A
treatmentisacombinationofaleveloffactorAandalevel
offactorB
1
Factor A
1
2
.
.
.
a
yijk=
Factor B
2
3
b
responseforthe
kthexp
(This project worth 10% of the total marks of the course. Please work in group and
submit a group report of up to 9 pages).
Project:
A maker of fabric for clothing is setting up a new line to finish the raw fabric. He is
interested to investigate the effe
Calculus II for Engineering
MIDTERM EXAMINATION
Fall, 2008
Section I. Multiple Choice Problems (Total 20 Points, 2 Points Each)
(No partial credits for this section)
1. (2 points) Find a vector with magnitude 4 in the same direction as the vector from the
Calculus II for Engineering
FIRST EXAMINATION
Fall, 2008
1. (Total 10) For a = 〈 1, 2 〉, b = 〈 5, −6 〉, c = i − 4j − 3k and d = i − 3j + 4k, compute
(1.1) (5 points) a + b and b − 2a
United Arab Emirates University
College of Sciences
Department of Mathem
Vectors
A vector is a line segment running from point A (tail) to point B (head).
Each vector has a magnitude (also referred to as length) and a direction.
Direction of a Vector
This is the direction of the line which contains the vector or any line which
United Arab Emirates University
College of Sciences
Department of Mathematical Sciences
MIDTERM EXAMINATION
Calculus II for Engineering
Exam Date: Monday, March 29, 2009
ID No:
200
Name:
Score:
/40
Instructions:
1. Read the questions carefully before you
Dot Product
Given the two vectors
the dot product is,
and
The dot product is also called an inner product
.
Example Compute the dot product for each of the following.
(a)
(b)
Solution
(a)
(b)
Here are some properties of the dot product.
Properties
If
then
Cross Product
Consider the two vectors
and
then the cross product is given by the formula,
The notation for the determinant is as follows,
Here is the way to do that formula.
where,
Another idea
We multiply along each diagonal and add those that move from
In[1]:=
Needs " VectorFieldPlots`"
In[2]:=
A
GradientFieldPlot Sin x y ,
B
ContourPlot
x,
1, 1 ,
y,
1, 1
Out[2]=
In[3]:=
Sin x y
.1, Sin x y
0, Sin x y
1.0
0.5
Out[3]=
0.0
0.5
1.0
1.0
0.5
0.0
0.5
1.0
.1 , x, 1, 1 ,
y, 1, 1
2
Untitled-1
In[4]:=
Out[4]=
Sho
United Arab Emirates University
College of Sciences
Department of Mathematical Sciences
EXAM 1
Calculus II for Engineering
MATH 1120 SECTION 4 CRN 23510
11:00 12:50 on Monday & Wednesday
Exam Date: Wednesday, September 24, 2008
ID No:
200
Name:
Score:
/80
STAT220
EngineeringStatistics
Unit8:
StatisticalInferenceforTwo
Samples
ComparingTwoVariances
For the comparison of two variances or standard
deviationsofnormalpopulations,anFtestisused.
Thesamplingdistributionofthevariancesiscalledthe F
distribution.
Cha
STAT220
EngineeringStatistics
Unit7:
Testsofhypothesesforasingle
sample
Introduction
There are two common types of formal statistical
inference:
1) Confidenceintervals(IntervalEstimation)
They are appropriate when our goal is to estimate a
populationparam
HW Assignment 1
Engineering Statistics (STAT220)
Section:
Spring 2011
Note:. Please solve all the questions. One problem will be chosen for grading.
NSTRUCTIONS:
I
1.
2.
3.
4.
Please solve the following problems and submit a group solution
Write down yo
Stat 220: Engineering Statistics
Spring 2011
HomeWork#2
Marks
obtained
Total
20
Name:_
IDNumber:_
NSTRUCTIONS:
I
OLVEALLTHEPROBLEMS.ONEPROBLEMWILLBECHOSENFORGRADING.
S
1. Write down your name and student ID.
2. Due on March 23 at the beginning of the cl
Stat 220: Engineering Statistics
Spring 2011
HomeWork#2
Marks
obtained
Total
20
Name:_
IDNumber:_
NSTRUCTIONS:
I
OLVEALLTHEPROBLEMS.ONEPROBLEMWILLBECHOSENFORGRADING.
S
1. Write down your name and student ID.
2. Due on March 23 at the beginning of the cl
HW Assignment 3
Engineering Statistics (STAT220)
Spring 2011
Note: Please solve the following problems and submit a group solution. This homework is due at the beginning of the
class on Wednesday, 27 April 2011. One problem will be chosen for grading.
Pro
HW Assignment 3
Engineering Statistics (STAT220)
Spring 2011
Note: Please solve the following problems and submit a group solution. This homework is due at the beginning of the
class on Wednesday, 27 April 2011. One problem will be chosen for grading.
Pro
HW4
EngineeringStatisticsSTAT220
Spring2011
Due: Monday, May 16, 2011
Solve all the problems. Two problems will be chosen for grading.
Problem1:Acompanythatsupportstwodifferenttypesofcomputernetworksisinterestedincomparingthe
meandowntimeforthetwotypes.A
HW Assignment 5
Engineering Statistics (STAT220)
Spring 2011
Note: Please solve the following problems and submit a group solution. This homework is due
at the beginning of the class on Monday, June 1, 2010. One problem will be chosen for grading.
Problem
Multiple Choice
1 points
Question Which of the following is NOT a possible probability?
Answer
25/1
00
1.25
1
0
Question 1
Multiple Choice
1 points
Question
Two events with nonzero probabilities
Answer
Question 3
can be both mutually exclusive and indepen
Question 1: Let X has cumulative distribution function
a) Compute the probability density function of X
b) Find P(-1/2X1/2)
c) Find P(X1/2)
Question 2: The total lifetime (in years) of an electronic device is a random variable with a pdf
a)
b)
c)
d)
e)
Fi
Question 1: Let X has cumulative distribution function
a) Compute the probability density function of X
b) Find P(-1/2X1/2)
c) Find P(X1/2)
Question 2: The total lifetime (in years) of an electronic device is a random variable with a pdf
a)
b)
c)
d)
e)
Fi
United Arab Emirates University
College of Business and Economics
STAT 220: Engineering Statistics
Spring 2011
Instructor: Dr. Shahadut Hossain
Office: Building C3, Room 1039
Tel: 03-7133429
E-mail: [email protected]
Class Time:
Section
Days
Time
Buildi
STAT220
EngineeringStatistics
Unit4:
ContinuousRandomVariables
Introduction
A random variable X is called continuous if its set of
possiblevaluesisacontinuumofvalues(e.g.anentire
intervalofnumbersiftherealnumbers a < b,thenany
numberxbetweenaandbispossibl