SS3657 Lecture 5
I
Review of the basic properties of cdf functions.
I
The properties of pdf and cdf of a continuous r.v.
I
Textbook coverage: Chap 2.2
1/9
Identify which of the following plots displays a valid cdf
(only ONE correct)
0.8
0.6
F(x)
0.4
0.2
0
SS3657 Lecture 1
Review old concepts with new perspective:
I Examples
I
I
The throwing two dices for a sum of 7;
The birthday problem
I
The concept of probability triplet (, F, P)
I
The axioms of probability
I
Textbook coverage: Chapter 1: 1.2-1.4
1/8
Pro
SS3657 Lecture 2
It is all about conditional probability
I Examples
I
I
The Polyas Urn model
The Monty hall problem
I
The definition of conditional probability
I
The Law of Total Probability
I
The Bayes Rule
I
Textbook coverage: Chapter 1: 1.5
1/9
The def
SS3657 Lecture 3
I
The concept of independence
I
I
I
I
Examples
I
I
I
Pairwise independence v.s. (mutually) independence
Physical independence v.s. statistical independence
Mutually exclusive events are actually dependent
The drawing a ball from 4 balls
T
SS3657 Lecture 4
I
The definition of random variables
I
The properties of cdf F ()
Discrete r.v.s
I
I
I
cdf and pmf of a discrete r.v.
Textbook coverage: Chap 2.1
1/17
The definition of random variable (rv)
I
I
Motivation: why do we need random variable i
SS3657 Lecture 1
Review old concepts with new perspective:
I Examples in the form of clicker questions
I
I
The probability of obtaining a sum of 7 when throwing two
dices
The birthday problem
I
The concept of probability triplet (, F, P)
I
The axioms of p
SS3657 Lecture 3
I
I
Examples in the form of clicker questions: circuit example.
The concept of independence
I
I
I
I
Pairwise independence v.s. (mutually) independence
Physical independence v.s. statistical independence
Mutually exclusive events are actua
SS3657 Lecture 6
I
Transformations or functions of a r.v.
I
Textbook coverage: Chap 2.3
1/14
Transformation Y = g(X)
I
Consider a transformation Y = g(X), where g is a function
g : D 7 R.
The domain D of g is typically the reals in R, but it must at
least
5
Simulation
Much of statistics relies on being able to evaluate expectations of random variables, and finding quantiles of
distributions.1 For example:
In hypothesis testing, the p-value of a sample is defined as the probability of observing data at lea
6
Computational Linear Algebra
Linear algebra deals with vector spaces and linear operations on them. In mathematics, we usually represent
vectors as column vectors of numbers, and linear operations as matrices. Applying a linear operation to a vector
bec
4
Programming with R
Programming involves writing relatively complex systems of instructions. There are two broad styles of programming: the imperative style (used in R, for example) involves stringing together instructions telling the computer
what to do
7
Numerical Optimization
In many areas of statistics and applied mathematics one has to solve the following problem: given a function f (),
which value of x makes f (x) as large or as small as possible?
For example, in financial modelling f (x) might be t
A First Course in Statistical Programming with R
W. J. Braun and D. J. Murdoch
January 5, 2016
Preface to the Second Edition
A lot of things have happened in the R community since we wrote the first edition of this text. Millions of new
users have started
Statistics 1023B (Statistical Concepts)
Winter 2015 Course Syllabus
Calendar Description
An examination of statistical issues aiming towards statistical literacy and appropriate interpretation of
statistical information. Common misconceptions will be targ
Department of Statistical and Actuarial Sciences. University of Western Ontario
Room 262 Western Science Centre. Phone: 519-661-3607. Fax: 519-661-3813
Statistical Programming 2014/2015
Statistical Science 2864B Section 001
Course Outline
Instructor Infor
Quiz 4
Statistics 2864 B
Copyright Jinkun Xiao & A. I. McLeod, 2015
Student performance
Test remarked and the scores are much improved. Four students received a perfect score. Students who were absent or received 0 were dropped from the statistical analys
Revised Solutions to Quiz 2
Statistics 2864, Copyright A. I. McLeod, 2015
The questions and answers below are not in the same order as appeared on the online version.
Due to a typo there were 2 correct answers to question 5.
115 students completed Quiz 2
Solutions to Quiz 1
Statistics 2864, Copyright A. I. McLeod, 2015
The questions and answers below are not in the same order as appeared on the online version.
The R code to produce the answers is shown in the last section.
There was an error in Question 2
Quiz 3 Solutions
Statistics 2864
Copyright A. I. McLeod, 2015
Comments on the Quiz
The Quiz is out of 4 since there was an error in Question 2, see comments below. The distribution
of scores is shown below. Out of 114 students, 73 received a perfect score