MATLAB Primer
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3/2
ans =
1.5000
3^2
ans =
9
2*pi
ans =
6.2832
2*37
ans =
1
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a=3
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CN3421: Applied Statistics for Engineers
Chapter 2: Introduction to Probability
Source: chapter 2
Applied Statistics for Engineers
Why do engineers need to know statistics?
Because engineers deal with data on regular basis. Real
life data are not perfect,
CN3421: Applied Statistics for Engineers
Designing Experiments with Several Factors
Lecture 9
Source: sections 14.114.2, 14.5
14
Chapter 14: Designing Experiments w/ Several Factors
Example:
Process yield in a CSTR is a function of the residence
time and
CN3421: Applied Statistics for Engineers
Joint Probability Distributions
and Data Description
Sources: Chapters 56
Analysis of Joint Probability Distributions
Th
Thus far, we have only considered a single random
variable (discrete and continuous). Reall
CN3421: Applied Statistics for Engineers
Ch
Chapter 5:
Analysis of Joint Probability Distributions
Sources: Sections 5.15.5
Chapter 5: Analysis of Joint Probability Distributions
Th
Thus far, we have only considered a single random
variable (discrete and
CN3421: Applied Statistics for Engineers
Statistical Inference
reading assignment: sections 6.1, 6.36.4, 6.6, 7.1, 7.2
Chapter 6: Random Sampling and Data Description
We often would like to know the populationlevel
th
parameters (mean, variance), which
CN3421: Applied Statistics for Engineers
Chapter 7: Point Estimation of Parameters
and Sampling Distributions
Sources: sections 7.17.2
Chapter 7: Point Estimation & Sampling Distributions
We use statistical inference to make decision or draw
conclusion f
CN3421: Applied Statistics for Engineers
Ch
Chapter 12:
12
Analysis of Multiple Linear Regression
Source: sections 12.112.3
Chapter 12: Analysis of Multiple Linear Regression
Th
There are many situations where we have more than one
th
regressor. For exam
CN3421: Applied Statistics for Engineers
Chapter 8: Analysis of Statistical Intervals:
Single Sample
Sources: sections 8.18.4
Chapter 8: Analysis of Statistical Intervals
We have learned that population parameters can be
estimated from a random sample, a
CN3421: Applied Statistics for Engineers
Ch
Chapter 11:
11
Analysis of Simple Linear Regression and Correlation
Source: chapter 11
Chapter 11: Simple Linear Regression and Correlation
We often gather data to explore the relationship
ft
th
between two or m
CN3421: Applied Statistics for Engineers
Test of Hypothesis
Sources: sections 9.19.2, 9.7, 10.110.2
Chapter 9: Test of Hypothesis: Single Sample
Th
The second topic in statistical inference concerns with
accepting or rejecting a statement about the popu
CN3421: Applied Statistics for Engineers
Ch
Chapter 14:
14
Designing Experiments with Several Factors
Source: sections 14.114.2, 14.5
Chapter 14: Designing Experiments w/ Several Factors
By now, we know how to:
(1) estimate population parameters from a r
Linear Regression
A Lesson from Drying Processes
How does the drying rate changes as a function of feeding rate,
temperature and humidity?
temperature, humidity
feeding rate
feeding rate
drying rate
= 1 + 2T + 3V + 4 H
temperature
humidity
Linear Regress
CN3421: Applied Statistics for Engineers
Analysis of Random Variables:
Probability Distributions
Sources: chapters 3 & 4
Analysis of Random Variables
Recall:
A random variable (RV) assigns a value to each outcome
in the sample space of a random experiment
CN3421: Applied Statistics for Engineers
Test of Hypothesis
Lecture 6
Sources: sections 9.19.2, 9.7, 10.110.2
Chapter 9: Test of Hypothesis: Single Sample
Th
The second topic in statistical inference concerns with
accepting or rejecting a statement abou
Systems of NonLinear
Equations
Examples of Nonlinear Equations
Characteristic equation in process control
1 + 4 s 16 s 2 + 3s 3 + 7 s 4 = 0
polynomial
Van der Waals eq.
2
n V
P + a b = RT
V n
complex expression
Friction factor f for the turbulent flow
Orthonormality of Vectors and
Functions
Vectors
a1
x = a2 column vector
a3
x = [ a1
a2
a3 ] row vector
( a1 , a2 , a3 )
x
x = a +a +a
2
1
( 0,0,0)
if
2
2
2
3
x = 1 then x is a unit
vector
Inner Products
a1
x = a2
a3
b1
y = b2
b3
x, y = a1b1 +
Eigenvalues and Eigenvectors
Solving First Order Ordinary Differential
Equations (ODEs)
How to solve
dx
ax = b
dt
First, we solve
dxh
axh = 0
dt
xh = ce
By observation
(ace at ace at = 0)
at
?
homogeneous solution
xp 0
b
Second, we solve
ax p = b x p =
Numerical Integration and
Differentiation
Approximation
curve
cow
straight line
sphere
constant
Taylor Theorem
If f(x) has (n +1) continuous derivatives in the interval [ a, b], then
( x x0 ) 2
f ( x ) = f ( x0 ) + ( x x0 ) f ( x0 ) +
( x x0 ) n+1
Rn +1 (
CN3421: Applied Statistics for Engineers
Point Estimation of Parameters
and Sampling Distributions
Lecture 4
Sources: sections 7.17.2
Chapter 7: Point Estimation & Sampling Distributions
An article in the J. Heat Transfer reported the thermal
th
th
condu
CN3421: Applied Statistics for Engineers
Chapter 8: Analysis of Statistical Intervals:
Single Sample
Sources: sections 8.18.4
Chapter 8: Analysis of Statistical Intervals
Statistical Intervals (Confidence Intervals: CI)
(C
CI)
CI on of Normal distributi
CN3421: Applied Statistics for Engineers
Introduction to Probability and Random Variables
Lecture 1
Source: Chapter 2
Applied Statistics for Engineers
Lectures and Tutorials:
Rudi Gunawan (E50216; [email protected])
Text: Montgomery & Runger, Applied Sta
CN3421: Applied Statistics for Engineers
Test of Hypothesis and
Analysis of Simple Linear Regression and Correlation
Lecture 7
Source: chapter 1011
Chapter 9: Test of Hypothesis: Single Sample
Summary:
Pr oblem Type
H0 : = 0
known
2
Test Statistic
z0 =
CN3421: Applied Statistics for Engineers
Analysis of Random Variables:
Single Variable
Lecture 2
Sources: Chapters 3  4
Analysis of Random Variables
Analysis of Random Variables: Single Variable
Si
Discrete vs. Continuous Probability Functions
Continuou
CN3421: Applied Statistics for Engineers
Analysis of Multiple Linear Regression
Lecture 8
Source: sections 12.112.3
Chapter 12: Analysis of Multiple Linear Regression
Multiple Linear Regression Model
A general linear regression model is given by
Y = 0 +
Models for
Thermal
& Thermal
Pave the way for heat control
:
Baowen Li ( )
Nonlinear and Complex Systems Lab
Department of Physics
1
IMS, 26 Nov 2004
Acknowledgement
Collaborators:
Lei Wang (Temasek Lab, NUS)
Giulio Casati (Como, Italy and NUS)
Financial