MTH 4106
Introduction to Statistics
Notes 12
Spring Semester 2015
Hypothesis testing
Introduction
Suppose that we have a random sample X1 , X2 , . . ., Xn from a distribution with parameter . Rather than wishing to estimate , we may want to make a hypothe
AT&T A Past Monopoly or Not?
A monopoly is when a single company owns a majority or the entire market share in the
industry. A monopoly occurs when a company has no competition or substitutes and when the industry
has barriers to entry for other similar c
Religion Assignment
The most important and absolutely indispensable experience:
In my opinion, the most important experience is the experience of obligation. The
experience of feeling the need to follow a rule is all about a persons ethical being. There i
Questions for the Accused Keri Jones (Hassam)
1. Hi Ms. Keri how are you doing today?
2. Is this the first time you are getting in trouble with the law?
Yes this is the first time. I have never even got in trouble at school before.
3. Can you explain me
Tiasha Bhuiyan
Cross Examination of Fiona Smith
1. You have worked for 5 years as a security guard at Muzik Box, is that
correct?
Anticipated answer: Yes
2. Of all the troublemakers you have caught in those five years, have majority
of them been youth?
An
Questions for Phil Jackson the witness Neveinth
1. Hi Mr. Jackson how are you doing today?
2. What kind of a student are you Phil?
- I am very intelligent. I have been on the honour roll since grade 9. And I am very passionate about
my school work and I a
Keri Jones
My name is Keri Jones, I am a 16 year old teenage girl. I am in high school, currently in grade 11.
I have no previous criminal record and have never been in any other type of real trouble. I am not known
to anyone as a troublesome child or per
Calculating GDP
Income and Expenditure
Approach
The Simple Circular Flow
Figure 8-1
2
The Simple Circular Flow
Figure 8-1
3
The Simple Circular Flow
Figure 8-1
4
The Simple Circular Flow
Figure 8-1
5
The Simple Circular Flow
Two observations
In every econ
B)
Report
Muhammad. A
Playing monopoly in class was a very fun experience which also taught me quite a few lessons
that can be helpful in the real world with my personal finances. I employed certain strategies from the
beginning of the game, which gave me
MTH 4106
Introduction to Statistics
Notes 9
Spring Semester 2015
Sampling distributions
If we have collected a random sample of size n, then X1 , X2 , . . . , Xn are independent random variables with the same distribution. Suppose that the distribution ha
MTH 4106
Introduction to Statistics
Notes 11
Spring Semester 2015
Estimating a proportion
Suppose that there is a population of N items, of which M have Type A and N M
have Type B. Put
M
= proportion having Type A.
p=
N
We take a random sample of size n.
MTH 4106
Introduction to Statistics
Notes 13
Spring Semester 2015
Interval estimation
So far, all of our estimates have been single numbers: these are called point estimates.
Sometimes, it is better to give interval estimates.
Definition If is a number as
MTH 4106
Introduction to Statistics
Notes 14
Spring Semester 2015
Conditional random variables
Discrete random variables
Suppose that X and Y have a joint discrete distribution. If P(Y = y) 6= 0, then we can
define the conditional probability
P(X = x | Y
MTH 4106
Introduction to Statistics
Notes 8
Spring Semester 2015
Sums of independent random variables
Theorems about the distribution of a sum
If X1 , X2 , . . . , Xm are independent random variables such that Xi Bin(ni , p) for i = 1,
2, . . . , m, and Y
MTH 4106
Introduction to Statistics
Notes 5
Spring Semester 2015
Continuous random variables
If X is a random variable (rv), then its cumulative distribution function (cdf) F is
defined by
F(x) = P(X 6 x)
for x R.
We write FX (x) if we need to emphasise t
MTH 4106
Introduction to Statistics
Notes 2
Spring Semester 2015
Exploratory data analysis
In Probability, we start with a probability distribution for some random variable X ,
and deduce things like the expectation E(X ) or P(X > 80).
In Statistics, we s
MTH 4106
Introduction to Statistics
Notes 4
Spring Semester 2015
Discrete random variables
Some revision
If X is a discrete random variable, then X may take
finitely many values x1 < x2 < . . . < xn
or
infinitely many values cfw_xi : i Z.
Write pi = P(X =
MTH 4106
Introduction to Statistics
Notes 7
Spring Semester 2015
Two or more random variables
Two continuous random variables
If X and Y are continuous random variables defined on the same sample space, they
have a joint probability density function fX,Y
MTH 4106
Introduction to Statistics
Notes 6
Spring Semester 2015
Normal random variables
As with uniform random variables, we deal first with the simplest case.
Standard normal random variable N(0, 1)
A continuous random variable Z is standard normal if i
MTH 4106
Introduction to Statistics
Notes 10
Spring Semester 2015
Simulation
Suppose that X , Y , Z, . . . are independent random variables whose distributions we
know. We want to find out the distributions of simple functions of these, like X 2,
X + Y ,
Underground
Economy
BY: C H R IST I A N C O R D EI R O
What is the Underground
Economy?
The Underground Economy (UE), is activity that is
under-reported or unreported for tax purposes.
In simple terms the UE is all the trade and work
that happens under
Market
Structure
s
Analyzing the levels of
competition in various
markets
Suppose you want to start
a new business
Review the scenarios on the next slide,
and decide under which conditions you
would prefer to start your business.
Give at least two reaso
Briefly outline any future career plans and aspirations you may have. (Max.
2000 characters)
Describe any extracurricular activities and employment experiences with
which you have been involved that you think demonstrate good citizenship
and leadership
Please submit an electronic copy of your application via email
to [email protected] by Monday, September 19th, 2016 at
8:00pm.
Save the document as Your Name_Friday Friends Application
Name:
Email:
Phone Number:
Year and Faculty:
Volunteers and adol
Stage 1: Separation
Ordinary World: Harry's parents died only when he was a baby, and has been living with his foster
parents, the Dursleys, ever since.
Call to Adventure: Harry's call for adventure comes when Hagrid shows up in his ordinary world and tel
SALAAR A
Research notes by Salaar
Haroun confronts him, asking "What's the use of stories that aren't even true?"
Utterly deflated by his son's loss of confidence in him, Rashid loses his gift for
communication. Haroun immediately regrets hurting his fath
Demand:
1. Summary of the article:
Apple is launching three new products in an upcoming event that seems quite pointless
since the new products are just an improvement of the products they recently came out with.
However, apple feels that they need an eve