Set Theory and Logic
Supplementary Materials
Math 103: Contemporary Mathematics with Applications
A. Calini, E. Jurisich, S. Shields
c
2008
2
Chapter 1
Set Theory
1.1
Basic definitions and notation
A set is a collection of objects. For example, a deck of
Econ 514: Probability and Statistics
Lecture 4: Independence
Stochastic independence
Random experiments may consist of stages that are performed independently.
Example: Roll a die two times. Consider the events
E1 = 1 or 2 on first roll
E2 = 2,3,5 on se
Maseno University
MAS 101/MMA 104: Descriptive Statistics
Lecture 2: Graphical Presentations
Lecture 2
SUMMARIZING A SINGLE CATEGORICAL VARIABLE
After the data have been collected, they can be consolidated and summarized to show the
following information:
Chapter 2
Abstract Algebra
83
part of abstract algebra, sets are fundamental to all areas of mathematics and we
need to establish a precise language for sets. We also explore operations on sets
and relations between sets, developing an algebra of sets tha
Joint probability is the probability that the RVs X & Y take values x & y.
like the PDF of the two events, x and y. We will denote a joint probability function as
PX,Y(x,y) = P(X=x Y=y)
Marginal probability of X is the probability that RV X has the value
Maseno University
MAS 101/MMA 104: Descriptive Statistics
Lecture 3: Measures of Location and Spread
MEASURES OF CENTRAL TENDENCY the typical value of the distribution
The overall pattern of the distribution of a quantitative variable is described by its
Maseno University
MAS 103: Introduction to Probability Theory
PROBABILITY DISTRIBUTIONS
A CONTINUOUS RANDOM VARIABLE
As mentioned earlier, the two important types of random variables are discrete and
continuous. In this Topic, we study the continuous rand
Maseno University
MAS 103: Introduction to Probability Theory
PROBABILITY DISTRIBUTIONS
A DISCRETE RANDOM VARIABLE
The probability distribution of a random variable
X
says how the total
probability of 1 is distributed among (allocated to) the various poss
Maseno University
MAS 103: Introduction to Probability Theory
LECTURE 7
THE MOMENT GENERATING FUNCTION
The Moment Generating Function is used to generate moments of random variables about
E ( Xr )
the origin, that is,
- the
r
th
moment of the random varia
MAS 103: INTRODUCTION TO PROBABILITY THEORY
Using formulae to answer probability questions (Practice questions)
Question 1
Question 2
Question 3
Question 4
Question 5
Question 6
Maseno University
MAS 101/MMA 104: Descriptive Statistics
Lecture 1
Lecture 1
What is Statistics?
Statistics is all about is converting data into useful information. It a process
where we are:
collecting data,
summarizing data, and
interpreting data
Th
Maseno University
MAS 103: Introduction to Probability Theory
EXPECTATION OF A RANDOM VARIABLE
Another View of Probability Mass Functions
It is often helpful to think of a probability mass function as specifying a mathematical model
for a discrete populat
Solution to Math Exercise 1
1.
Eulers Theorem
(a) Show that Eulers Theorem holds for a constant returns to scale
(CRTS) production function F (x1 , x2 ) with two factors of production x1 and x2 .
F (x1 , x2 ) = F (x1 , x2 )
F (x1 )
F (x2 )
+
= F (x1 , x2
Answers
hypothesis test? is a statistical test that is used to determine whether there is enough evidence in a
sample of data to infer that a certain condition is true for the entire population. A hypothesis test
examines two opposing hypotheses about a p
YOU MUST FIRST USE THE ATTACHMENT FILE FOR ESTATE PLANNING BOOK, IF YOU
DONT FIND THE ANSWER IN THE CHAPTER FILES YOU CAN USE OTHER (ONLINE WRITTEN
MATERIAL) BEASED ON ESTATE PLAINNING SUBJECT TO ASSIST YOU IN ANSWERING THE
QUESTIONS. PLEASE: I NEED A HIG
Reliability and validity are related qualities but independent. They are similar to the terms
"precision" and "accuracy," respectively. A wind-up clock that does not work is accurate
(valid) twice a day. But it lacks precision (reliability). A digital clo
Surname1
Name
Institution
Professor
Class
Date
Three movie documentaries analyzing in details
Looking at the case of the documentary, Vincent Who one notes that
biographical Vincent resembled a Japanese man despite being a Chinese. Vincent was
murdered in
TITLE
SURNAME
INSTITUTION
DATE
1: Rawles (2008) explains to the President how beneficial it was for him to have had
teachers who were passionate about what they taught. This is my experience too. I believe
there is merit to the idea of a national standard
MASENO UNIVERSITY
UNIVERSITY EXAMINATION 2011 / 2012
FIRST YEAR EXAMINATION FOR THE DEGREE OF MASTER OF SCIENCE IN
RESEARCH METHODS (E-LEARNING)
MRM 837: DESIGN AND ANALYSIS OF SURVEYS 1
Instructions:
This paper consists of FIVE Questions
Answer any THR
Running head: DIGITAL MARKETING
1
Live Capstone Digital Project on Lifcare Pharma
Name
Institutional Affiliation
DIGITAL MARKETING
2
Introduction
Lifcare Pharma is a start-up pharmaceutical company based in India, which was founded
in 2015. It is a subscr
Due in on July 30, 2016 @ 12:00AM
BAF1101 FINANCIAL ACCOUNTING I ASSIGNMENT MAY-AUG 2016
QUESTION ONE
The following trial balance has been extracted from the ledger of Ndoto ndogo, a sole trader
Ndoto ndogo Trial Balance for the year ended 31 May 2014
Sal
COMMUNICATION
1
CLINICAL APPLICATION FOR COMMUNICATION
SURNAME
PROFESSOR
INSTITUTION
DATE
COMMUNICATION
2
INTRODUCTION
Communication is the process by which information and ideas are exchanged by two different
parties that is from the sender to the receiv
Creating a Coding Variable in SPSS
Suppose that you are entering data in SPSS and you have two more groups of
scores. You want to create a variable that indicates, for each case, to which group the
case belongs, but you do not want to bother with typing i
Surname1
Name
Professor
Institution
Course
Date
Introduction
Land was taken as something important among the Africans , they used the land for cultivation
and the keeping of livestock ,these two activities were the main source of food for the Africans
thu
1
Title: ideas by George Lucas in relation to The Great Gatsby
Name:
Class information:
Date:
2
Marx in his work he states that the theory becomes a force of material when it happens to grasp
the masses. The features and the definition both of the theory
STATISTICS
1
STATISTICS
NAME
INSTISTUTION
STATISTICS
FINDINGS AND INTERPRETATION
According to the attached excel files, the following was found:
The correlation coefficient between the weight and GHG was 0.8896.This figure means that is a
perfectly positi
Running Head:
Discrepancy Diagnosis 1
TITLE
SURNAME
INSTITUTION
DATE
Running Head:
Discrepancy Diagnosis 2
Further questions Laura at the first visit
Various questions are crossing and running on Lauras mind and she thinks that she is suffering
form a par