CONCEPTUAL TOOLS
EX:
P ROBABILITY
JOINT PDF, f(x,y)
Example 2
By: Neil E. Cotter
A joint probability density function is defined as follows:
k
f (x, y) =
0
x2 + y2 1
otherwise
a)
Sketch the shape of f(x,y). (You may assume k = 1 for this sketch.)
b)
Calc
MA0461- PROBABILITY & STATISTICS
Name of the student :
Prepared by
Dr.N. BALAJI
Asst. Professor (SG)
Department of Mathematics
Faculty of Engineering & Technology
SRM UNIVERSITY
For the students of VIIth sem Mechanical Engineering
2015-16 (ODD SEM)
MA0461
WhatisPython
Python is
an
object-oriented,
high
level
language,
interpreted,
dynamic
and
multipurpose
programming language.
Python is easy to learn yet powerful and versatile scripting language which makes it attractive for
Application Development.
Python
W&M CSCI 628: Design of Experiments
Homework 1
Megan Rose Bryant
September 2, 2014
1.2
Suppose that you want to investigate the factors that potentially affect cooking rice.
a.)What would you use as a response variable in this experiment? How would
you me
Developing
Windows-Based
and Web-Enabled
Information Systems
Developing
Windows-Based
and Web-Enabled
Information Systems
Nong Ye
Teresa Wu
Boca Raton London New York
CRC Press is an imprint of the
Taylor & Francis Group, an informa business
CRC Press
Tay
Chapter 5. Entity-Relationship Modeling
for Conceptual Data Modeling
NONG YE and TERESA WU
Developing Windows-based and Web-Enabled Information
Systems
1
Overview
An entity-relationship (E-R) model organizes
data using entities, relationships and their
a
IEE 506 Web-enabled Decision Support Systems
Time and Location: TTH 1:30 AM 2:45 PM, COOR L1-10
Instructor:
Office:
Email:
Phone:
Office Hour:
Professor Nong Ye
BYENG 482
[email protected]
(480) 965-7812
Tuesdays 12 1 PM, and by appointment (an appointment m
COURSE SYLLABUS
IEE 572 DESIGN OF ENGINEERING EXPERIMENTS
Fall 2016
All Sections
Instructor: Professor D. C. Montgomery, BYENG 348, office phone 480.965.3836
Office hours: My office hours are Tuesday and Thursday afternoons, 12:30 1:15 PM
(most weeks). I
Chapter 2 Supplemental Text Material
S2.1. Models for the Data and the t-Test
The model presented in the text, equation (2.23) is more properly called a means model.
Since the mean is a location parameter, this type of model is also sometimes called a
loc
DECISION MAKING
FOR A SINGLE SAMPLE
Chapter 4
STATISTICAL INFERENCE
Statistical Inference helps us
determine information (like
mean, variance) about a
population based upon data
taken from a sample of size n
of that population
2
PARAMETER ESTIMATION
x
n
x
1
Chapter 1: Introduction to Statistics (Part 1)
What is Statistics?
Example No. 1
Political polls: Predicting the outcome of an election
Question: How could a political pollster predict the outcome
of a race for governor between candidates Smith and Jone
1
Chapter 2: Summarizing Information for
Single Variables (Part 4)
Measures of Position
z scores
Also called a standard score or standardized score, the
z score represents the number of standard deviations that a
given value of y falls above (or below) th
1
Chapter 2: Summarizing Information for
Single Variables (Part 3)
It is useful to have terms that describe the shapes of data
distributions as represented by histograms (or dot plots).
Terms used to describe distributional shapes (see handout)
1. Symmetr
1
Chapter 3: Introduction to Probability (Part 4)
We have learned how to use tables of the standard normal
distribution. In order to compute probabilities for normal
distributions having any mean and standard deviation we
need to learn some results about
1
gChapter 2: Summarizing Information for
Single Variables (Part 1)
Summarizing Quantitative Data with Tables and Graphs
Example: In a class of 20 students, the values of the variable
Course Grade were as follows (imagine the students are listed
in alphab
1
Chapter 2: Summarizing Information for
Single Variables (Part 2)
In addition to representing quantitative data with tables and
graphs, it is also useful to summarize the data by computing
quantities called parameters (if the data is considered as
popula
1
Chapter 2: Summarizing Information for
Single Variables (Part 5)
Dichotomous Variables
Consider a dichotomous variable D (defined with regard to
some population) taking on the values 0 and 1, with
p = Pr(D = 1) and
1 p = Pr(D = 0).
Example
Population: R
1
Chapter 1: Introduction to Statistics (Part 2)
Example No. 2
Question: Do men and women tend to weigh the same?
(What men and women are we talking about? What do we
mean by tend to weigh the same?)
Statistical Perspective
Population: Students enrolled a
1
Chapter 3: Introduction to Probability (Part 2)
Mathematical functions are often used to represent probability
distributions. These functions are of two distinct types:
1. Discrete functions
e.g. Binomial distributions
2. Continuous functions e.g. Norm
1
Chapter 1: Introduction to Statistics (Part 3)
Simple Random Sampling (revisited)
Recall the 3 by 5 inch index cards in a barrel mechanism for
obtaining a simple random sample that was discussed in Part 1.
One important detail that was omitted is the fa
1
Chapter 1: Introduction to Statistics (Part 4)
Types of Variables
It should be noted that other instructors or textbooks often
classify variables in a different way.
Quantitative variables
1. Continuous (also known as measurement)
Examples: Weight, Heig
1
Chapter 3: Introduction to Probability (Part 6)
Relationship Between Two (Dichotomous) Variables
Example
Population: U.S. Senators in 1993 (N = 100)
Variables: 1. Gender (Male or Female)
2. Party (Democrat or Republican)
Raw data
No. Gender
1
Male
2
Fem
1
Chapter 3: Introduction to Probability (Part 7)
Simpsons Paradox
Example: Is there gender bias with respect to graduate
school admissions?
All Students
Male
Female
Total
Admit Not Admit
233
324
88
194
321
518
Total
557
282
839
Pr(Admit | Male) = 233 / 5
1
Chapter 1: Introduction to Statistics (Part 5)
Overview of the Course
Chapter 1: Introduction to Statistics
Chapter 2: Summarizing Information for Single Variables
Chapter 3: Introduction to Probability
Chapter 4: Sampling Distributions
Chapter 5: Infer
1
Chapter 3: Introduction to Probability (Part 3)
Consideration of the binomial distribution has shown us how
discrete functions can represent probability distributions. We
will now consider the normal distribution, in which a
continuous function is used
1
Chapter 3: Introduction to Probability (Part 1)
Consider again the population of N = 20 students in a class,
for which we have the following relative frequency
distribution with respect to the variable Y = Grade Point:
y
Pr(Y = y)
0
.05
1
.15
2
.35
3
.3
1
Chapter 3: Introduction to Probability (Part 5)
The Normal Approximation to the Binomial Distribution
Under certain conditions, a binomial distribution can be well
approximated by a normal distribution. Specifically, if
Y ~ B( p, n), then (approximately
Exam 2 review
Solutions are on Blackboard.
Chapter 12 Regression and
Correlation
Weve compared so far:
2 Populations, ANOVA
And now Regression
Simple Linear Regression
Looking for relationships among two or more variables
So we observe the variables with