MTH 262 Probability theory and
random Variables
MTH 161 Introducton to Statstcs
Regression and Correlaton
We are often interested whether two variables are related.
In case they are; how they are related.
Linear Regression and Correlaton are two common
MTH 262 Statistics and Probability Theory
Probability Theory
We studied two types of Statistics (Descriptive and Inferential)
Inferential Statistics deals with method of drawing conclusions
about the population based on information from a sample.
Uncer
MTH 262 Statistics and Probability
Theory
Topic:
Sample space and Counting number of
Sample points in the sample space
Sample Space:
Collection of all possible outcomes
of a random experiment is called
Sample Space.
Examples
Flipping a single coin.
SS=cf
MTH 262 Statistics and Probability
Theory
Spring 2014
The Poisson distribution is used to model the frequency with which a specified
event occurs during a particular period of time.
For Example:
the number of patients who arrive at an emergency room betw
MTH 262 Statistics and Probability
Theory
Spring 2014
Lecture 19
MTH 161 Introduction to Statistics
Continuous Distribution
Continuous Random Variable
A random variable that can take any possible value in a given interval is called a
continuous random var
MTH 262 Statistics and Probability Theory
Spring 2014
Lecture 7
Last Lecture
Experiment:
By an experiment, we mean an action whose
outcomes cannot be predicted with certainty.
Event: An event is collection of one or more possible outcomes of an
experime
Statistics and Probability Theory
Spring 2014
Lecture 10
Abdul Wakeel
Conditional Probability
The probability that event B occurs given that event A occurs
is called a conditional probability
Denoted by P(B | A): Probability of B given A
A is called th
MTH 161 Introduction to Statistics
Spring 2014
Lecture 4
ABDUL WAKEEL
Dispersion
Measures the spread of data
Measure of center does not tell the whole story
Zero when all the values are same
Consider the two histograms below
Dispersion
Measures the s
Review of The Last Lecture:
Statistics.
Def, Branches,
Data, Primary and Secondary Data,
Collection and Presentation of Data.
POPULATION VS SAMPLE
POPULATION
includes all objects of interest that have common
characteristics
Parameter - characteristic o
MTH 262 Statistics and Probability Theory
Spring 2014
ABDUL WAKEEL
Mathematics Department
About Me
Quaid-i-Azam University
PMAS Arid Agriculture
2
Books
Introduction to Statistics (Reference Book)
Probability and Statistics for
Engineers and Scientists
(R
MTH 262 Statistics and Probability Theory
Spring 2014
ABDUL WAKEEL
Representation of Data
Data Array
Frequency Distribution
Histograms
Frequency Polygons
Ogives
Data Array
In a data array, the data is arranged in a ascending or
a descending order.
S
Statistics and Probability Theory
Spring 2015
Lecture 17
Abdul Wakeel
Announcements
Read all the lecture slides and book topics carefully.
Always define events before solving the question.
Statistics and Probability Theory
Sessional Exam II will includ
MTH 262 Statistics and Probability
Theory
Spring 2015
Lecture 22
Abdul Wakeel
Continuous Distribution
Statistics and Probability Theory
Continuous Random Variable
A random variable that can take any possible value in a given interval is called a
continuou
Statistics and Probability Theory
Spring 2015
Lecture 18
Abdul Wakeel
The Poisson Distribution
Statistics and Probability Theory
Abdul Wakeel
The Poisson Distribution
Statistics and Probability Theory
The Poisson distribution is used to model the frequenc
MTH 262 Statistics and Probability
Theory
Spring 2015
Lecture 12
Abdul Wakeel
The Law of Total Probability
Example
Suppose that a Management Science student is selected at
random. He/she can be bachelors, masters or PhD student.
E2 = a masters student is
MTH 262 Statistics and Probability
Theory
Spring 2014
Binomial Probability Formula
Let X denote the total number of successes in n Bernoulli trials with success
probability p.
MTH 161 Introduction to Statistics
Discrete Probability Distributions
Shahzad F
Statistics and Probability Theory
Spring 2014
Lecture 12
Abdul Wakeel
Conditional Probability
The probability that event B occurs given that event A occurs
is called a conditional probability
Denoted by P(B | A): Probability of B given A
A is called th
Statistics and Probability Theory
Fall 2014
Abdul Wakeel
MTH 161 Introduction to Statistics
Introducing Random Variables
Shahzad Fazal Bhat
Consider a class of 40 students. Professor asks the students to state how many
siblings they have.
MTH 161 Introduc
1217
9 Lehmann U, Blom W, Dlanjwa M
et al. Capacity development
through reflective practice and collaborative research among clinic
supervisors in rural South Africa a
case study. Educ Health 2004;17:53
61.
10 Rogers E. Diffusion of Innovations.
New York:
FREQUENCY
DISTRIBUTIONS
AND
PERCENTILES
New Statistical Notation
Frequency (f): the number of times a score
occurs
N sample size
N:
l i
Simple
Frequency Distributions
Raw Scores
The scores that we have directly measured.
measured
number of correct ans
The One-Sample t-Test
1
A brief history of the t-test
Just past the turn of the nineteenth century, a
major development in science was fermenting
at Guinness Brewery.
William Gosset, a brewmaster, had invented a
new method for determining how large a
samp
Correlation and Covariance
James H. Steiger
Goals for Today
Introduce the statistical concepts of
Covariance
Correlation
Investigate invariance properties
Develop computational formulas
Covariance
So far, we have been analyzing summary
statistics that de
Page 1 of 10
Chi Square Tutorial
Prof. Jeff Connor-Linton
Department of Linguistics
Georgetown University
[email protected]
Note: For this tutorial to display properly, your browser must support tables and should support superscripts (e.g. 3 squared
Lecture #1
Statistics is the study of the collection, organization, analysis,
interpretation, and presentation of data
Descriptive statistics: Statistical methods can be used for summarizing or
describing a collection of data; this is called descriptive s
CHI-SQUARE TEST
Adapted by Anne F. Maben from "Statistics for the Social Sciences" by Vicki Sharp
The chi-square (I) test is used to determine whether there is a significant difference between the expected
frequencies and the observed frequencies in one o
Answer the Following Problems
Problem No# 1 :
The table below lists the results of a student survey pertaining to favorite
ethnic foods. Each student chose only one type of ethnic food for the survey.
Type
Italian Chinese Japanese Thai Mexican Other
Numbe