ENG1060: Computing for Engineers
LECTURE 0
Welcome to ENG1060
Slides made by: Dr. Wai Ho Li
Lectured by: Dr. Y Hong
Clayton Unit Staff
Unit Overview
What is
Engineering
Computing?
Lecturer and coordinator
Dr. Yi Hong
Email: [email protected]
TODO: Wee
ENG5001/ENG6001
Advanced Engineering Data Analysis
Cumulative distribution function
I
An alternative method to describe the distribution of a
random variable is through the cumulative distribution
function (CDF in short), which is defined as the function
ENG5001/ENG6001
Advanced Engineering Data Analysis
Continuous uniform distribution
I
A random variable X is said to have a uniform distribution
over the interval [a, b] if its PDF is given by
f (x) =
I
1
,
ba
a x b.
If X is a continuous uniform random var
ENG5001/ENG6001
Advanced Engineering Data Analysis
ENG5001/ENG6001
Advanced Engineering Data Analysis
Chapter 5
Multivariate Random Variables
Joint distributions
I
I
If X and Y are two random variables, the probability
distribution that defines their simu
ENG5001/ENG6001
Advanced Engineering Data Analysis
Box plots
I
A box plot, also called box-and-whisker plot, displays the
five-number summary on a rectangular box, aligned either
horizontally or vertically.
Example
(Cotton content of fabric.) The five-num
ENG5001/ENG6001
Advanced Engineering Data Analysis
Probability
I
I
Probability is a number between zero and one that is used to
quantify the likelihood, or chance, that an outcome of a
random experiment will occur.
The probability of an outcome can be int
ENG5001/ENG6001
Advanced Engineering Data Analysis
Moments
I
E[X k ] is called the kth moment of X and is given by
X
E[X k ] =
x k f (x), if X is discrete with PMF f ,
x
E[X k ] =
Z
x k f (x)dx,
if X is continuous with PDF f .
Moment generating function
I
ENG5001/ENG6001
Advanced Engineering Data Analysis
Example
A class in probability theory consists of 6 men and 4 women. An
exam is given and the students are ranked according to their
performance. Assuming that no two students obtain the same
score, (a) h
(the following takes place in Giza, Egypt. The year is 2630 BC.Einstein has managed to travel back in
time to when the Great Pyramid of Giza was being constructed. He lands at the kings palace.)
Pharaoh: (Pacing around the room, talking to himself) I do n
I Hate writing because.
I hate writing because it is a tedious and dirty job.
I hate writing because it is a really messy job
My hands, pants and shirts all get dirty and messy, because of the ink from the pens.
Writing is an outdated form of art,
Outdate
ENG5001/ENG6001
Advanced Engineering Data Analysis
Discrete uniform distribution
I
A random variable X is said to have a discrete uniform
distribution if each of the n values in its range, say,
x1 , x2 , . . . , xn , has equal probability. Its PMF is give
ENG5001/ENG6001
Advanced Engineering Data Analysis
Categorical data (two variables)
Example
A company operates four machines in three shifts each day. From
production records, the data on the number of breakdowns are
collected and summarised in the follow
ENG5001/ENG6001
Advanced Engineering Data Analysis
Linear combination of random variables
I
Given random variables X1 , X2 , . . . , Xk and constants
c1 , c2 , . . . , ck , let
Y = c1 X1 + c2 X2 + + ck Xk .
I
E[Y ] = c1 E[X1 ] + c2 E[X2 ] + + ck E[Xk ]
I
ENG1060: Computing for Engineers
LECTURE 15
Curve Fitting
Linear Regression
Lecturer: Prof. Murray RUDMAN
Recap
Recap
Dealing with
Real Data
Statistics
Review
Linear
Regression
Fitting
Nonlinear
Models
Choosing a
Model
Root Finding
Bracketing Meth
ENG5001/ENG6001
Advanced Engineering Data Analysis
ENG5001/ENG6001
Advanced Engineering Data Analysis
Chapter 1
Introduction
Why do we study statistics / data analysis?
I
I
We live in the era of Big Data.
Need to predict the future based on analyzing past
ENG5001/ENG6001
Advanced Engineering Data Analysis
Independence
I
By analogy with independent events, two random variables are
said to be independent if
fX ,Y (x, y ) = fX (x)fY (y )
for all x and y , where f s are PMFs in the discrete case or
PDFs in the
SPORTS IN OUR LIVES.
A sport is regarded as an activity involving physical exertion and skill in which an individual or team
competes against another or others for entertainment. In one way or another we all participate in the
world of sports. Directly by