Group Task
Create a printadvertisementlor any product or service the advertisement should contain text as
well as visuals.
You cant use an existing brand name or any existing advertisement be original
You should make a logical claim ll: have an attention-
Writing an Argumentative
Research Essay
A Step-by-Step Process
1. Find an interest in a broad subject area
2. Narrow the interest to a plausible topic
3. Question that topic from several points of
view
4. Develop a research question
5. Define a rationale
MATH 230-Probability
Quiz 5
Date: December 5, 2016
Name
Student ID
Useful Formulas:
If X Exponential(), f (x) = ex for x 0. E(X) = 1 , V ar(X) =
1
2 .
Let X be a positive continuous random variable. Hazard rate function (t) of
fX (t)
X is defined as (t)
Fantasy books, movies and T.V shows
like Harry Potter Series, Twilight, The
Vampire Diaries, Supernatural, A
Song of Ice and Fire, Eragon etc. are
damaging the developing minds and
personalities of teenagers
Terrorism, increasing disparity between the ric
Persuasion & Argumentation
What exactly is an argument?
Toughguy makes better trucks than
Strongman.
Toughguy makes better trucks than
Strongman because Toughguys trucks
are more reliable & last longer.
Assertion = just a claim with no reasons
Argument =
Rhetorical / Critical Analysis
How long have you been sitting in front of the television getting fat and lazy?
Wouldn't you like to find a means of exercise that will shape your body while you
are reading, watching television, or otherwise occupying your
Lahore University of Management Sciences
MATH 230 - Probability
Fall 2016
Instructor
Office Hours
Email
Telephone
Secretary/TA
TA Office Hours
Course URL
Faiza Khan, Jawad Ahmad Raheel
TBA
faiza.khan@lums.edu.pk, jawad.raheel@lums.edu.pk
TBA
TBA
TBA
LMS
C
Critical Thinking & Reading
Is Critical Thinking a Very Complicated Skill?
No, Honey, I dont want you to spend a lot of money on my birthday present. Just
having you for a husband is the only gift I need. In fact, Ill just drive my old rusty
bucket of bol
MATH 230-Probability
Azmat Hussain
Summary-Lecture 3
As we discussed in class 3, for a random variable X, in general, we have,
E (g(X) 6= g(E(X)
(1)
However, if g(X) = aX + b i.e. if g(X) a linear function of the random variable X, then
E (aX + b) = aE(X
MATH 230-Probability
Quiz 4a
Due: November 16, 2016
Name
Student ID
1. Let X be a continuous random variable with probability density function given
by
(
xk2 1 x 2
fX (x) =
0
otherwise
(a) (2 pts) Find the constant k so that fX (x) is a valid density fun
Sample Topics for the Final Argumentative Research Essay
These topics need to be focused into argumentative & researchable research questions.
Evolution vs creationism
Multiple personality disorder
Atlantis
Arthurian legend
ESP
Stigmata
Subliminal message
MATH 230-Probability
Azmat Hussain
Summary-Lecture 09
Jointly distributed random variables
Sum of independent random variables
Jointly Distributed Random Variables
Recall: If X and Y are both random variables defined on the same sample
space S, we say X
MATH 230-Probability
Azmat Hussain
Summary-Lecture 08
Hazard Rate function of a positive random variable
Jointly distributed random variables
Hazard (Failure) rate functions
What is a positive continuous random variable.
What does hazard rate function
MATH 230-Probability
Azmat Hussain
Summary-Lecture 10
Jointly distributed random variables
Sum of independent random variables
Conditional probability distribution
Sum of independent random variables
If X and Y are two independent random variables with
Academic Writing Style
Features of Academic Writing
achieving a balance between using more formal
language & maintaining some sense in your
own voice within the academic register
Writing Effective Sentences
Choosing Appropriate Words
Avoiding Figurativ
PARAGRAPH
DEVELOPMENT:
Unity, Relevance & Coherence
The basic purpose of a paragraph is to communicate some
information to the reader.
A communicatively sound paragraph displays the three
essential qualities of:
Completeness: i.e. provides an optimal leve
WRITING CONCLUSIONS
A Conclusion Should.
stress the importance of the thesis
statement
give the essay a sense of completeness
leave a final impression on the reader
Introduction
General
Specific
Conclusion
Specific
General
Strategies for taking the con
MATH 230-Probability
Quiz 4b
Date: November 16, 2016
Name
Student ID
1. Suppose that Faryal and Samina (best friends) live in the same neighborhood
in Lahore and they both leave for home from LUMS at 3:00 pm. Samina has a
car and she drives to LUMS everyd
Writing an Academic Essay:
introductions
&
thesis statements
The introduction has five main purposes:
to present the thesis or central idea of the essay
to lead in to this idea by describing the major issues the writer
is concerned with, giving any nece
MATH 230-Probability
Azmat Hussain
In Class Problem Set-Normal Random Variable
Let Z be a standard normal random variable (or we write Z N (0, 1). The
z2
pdf of Z is fZ (z) = 12 e 2 . Find
1. E(Z) =
V ar(Z) =
2. CDF: FZ (z) = P (Z z) = (z) = . . .
3. P (Z
MATH 230-Probability
Azmat Hussain
Summary-Lecture 5
General Normal Random Variable X N (, 2 )
1
PDF (Probability Density Function)
The probability density function of a Normal Random Variable X with parameters
and 2 is given by
2
1
(x)
2
2
fX (x) = e
(
MATH 230-Probability
Azmat Hussain
Summary-Lecture 6-7
Normal Approximation to Binomial Random Variable.
Exponential Random Variable.
We did the following in detail:
The Normal Approximation to Binomial Distribution
Why this approximation makes sense.
MATH 230-Probability
Azmat Hussain
Summary-Lecture 12
Conditional distributions
Properties of Expectations
Conditional probability distribution
We discussed the conditional probability distribution for discrete and continuous random variables.
If X and
MATH 230-Probability
Quiz 5
Date: December 02, 2016
Name
Student ID
Useful Formulas:
If X Exponential(), f (x) = ex for x 0. E(X) = 1 , V ar(X) =
1
2 .
Let X be a positive continuous random variable. Hazard rate function (t) of
fX (t)
X is defined as (t
MATH 230-Probability
Quiz 6
Due: anytime before December 16, 2016
Name
Student ID
1. The joint density function of X and Y is given by
(
1
xexy 0 < x < 2, 0 < y <
f (x, y) = 2
0
otherwise
(a) (3 pts) Find P (X < 1, Y < 1).
(b) (5 pts) Find P (X > Y ).
(c
SS 100 WRITING & COMMUNICATION
Essay 3
Fall 2015
Argumentative Research Essay
Choose a worthwhile, debatable, controversial topic that has adequate support from experts in the field.
Develop a thesis statement that clarifies your claim / point of view abo
MATH 230-Probability
Azmat Hussain
Summary-Lecture 4
The PDF (Probability Density Function) of Standard Normal random
variable Z is given by
z2
1
fZ (z) = e 2
(1)
2
For it to be a valid density we proved in the class that
Z
z2
1
e 2 dz = 1,
2
i.e. the
WRITING A PERSUASIVE /
ARGUMENTATIVE
ESSAY
In persuasive or argumentative writing,
we try to:
.convince others to agree with our facts,
.share our values,
.accept our argument and conclusions,
.adopt our way of thinking.
Some persuasive/argumentative essa
Common Logical Fallacies
Senator Jones' bill on gun control should not be taken seriously; after
all, this is the same man who has had at least five extramarital affairs.
AD HOMINEM ARGUMENTS attack the opponent rather than his or
her argument. (Ad homine