The Binomial Distribution
While we have been talking a bit about discrete probability distributions in general over the last two
sections, let us look at one particular distribution.
Quick note: your text refers to Bernoulli trials. Bernoulli is a special
Areas Under the Standard Normal Curve
So, how do we actually find probabilities for a normal distribution? We will answer this question only for
standard normal random variables to start.
Some properties of standard normal curve:
1. The total area under t
Some Rules of Probability
Now, a couple of rules for probability. One of these, we have already seen with our example involving
rolling a non-8 in the last section:
Complement rule: P(E) = 1 P(not E)
(General) Addition rule: P(A or B) = P(A) + P(B) P(A &
Math 140 Midterm Summer Session 2 2016 Prof. Simpson
Name: _
You have 2 hours to complete this test. You are allowed your calculator and the set of tables distributed
with the exam. Any other notes or aides are strictly forbidden! Be sure to show all of y
Discrete Random Variables and Probability Distributions
We will now start looking at random variables, which are quantitative variables whose value depends on
chance (a combination of both Chapters 2 and 3 data analysis and Chapter 4 probability). There a
The Mean and Standard Deviation of a Discrete Random Variable
When we talk about a discrete random variable, we can talk about center and variation, just like for a set
of data. This gives us a distinction between probability distributions and probabiliti
Events
First, for those of you not familiar with a deck of cards, please see the diagram of all cards given on page
165.
In this section, we are going to be a bit more precise with a couple of terms we used in the last section.
The sample space consists o
Assessing Normality; Normal Probability Plots
So far, we presumed that our data was normal. If given a set of data, can you tell if it is normal? We can
by drawing a normal probability plot (or normal quantile plot).
What do we want to see with these plot
Introducing Normally Distributed Variables
We now turn our attention to some continuous random variables. While there are many that we could
consider, we will focus on just one the normally distributed continuous random variable.
We have already talked ab
Working with Normally Distributed Variables
So far, we have not had any applications of normal distributions we just looked at the table to
determine probabilities. That is about to change.
To determine a probability for a normally distributed variable:
1
Probability Basics
We will now take a look at some ideas from probability. We wont be going into very much depth with
regards to probability, but it is important to have a good grasp on the basics. The computations are going
to be (relatively) straightfor
MATH 116
Prof. Houston
Module 10
Number Bases and Base Conversions
Objectives
By the end of this module, students will be able to:
Comprehend what is meant by a base b positional system.
Convert a number from base b to base 10.
Convert a number from base
MATH 116
Prof. Houston
Module 19
Prime and Composite Numbers
Objectives
By the end of this module, students will be able to:
Apply the definitions of prime and composite numbers.
Use the Sieve of Eratosthenes to find prime numbers.
Use Goldbachs Conjec
MATH 116
Prof. Houston
Module 28
Systems of Linear Equations Modern Methods
Objectives
By the end of this module, students will be able to:
Solve systems of linear equations in 2 variables using modern methods (review).
Solve systems of linear equations i
MATH 116
Prof. Houston
Module 2
Babylonian Cuneiform Numeration System
Objectives
By the end of this module students will be able to:
Given a number in the Babylonian Cuneiform numeration system, write the number
in the Hindu-Arabic numeration system.
Giv
MATH 116
Prof. Houston
Module 1
Hindu-Arabic Numeration System
Objectives
By the end of this module students will be able to:
Explain what is meant by a numeration system.
Describe the four types of numeration systems that will be covered in this course
MATH 116
Prof. Houston
Module 33
Square Roots Interpolation Method
Objectives
By the end of this module, students will be able to:
Find square roots by the interpolation method.
Assignments
Read Module 33
Complete the Problem Set for Module 33
MATH 116 Mo
MATH 116
Prof. Houston
Module 25
Linear Equations False Position
Objectives
By the end of this module, students will be able to:
Solve linear equations using the False Position method.
Assignments
Read Module 25
Complete the Problem Set for Module 25
Intr
MATH 116
Prof. Houston
Module 31
Diophantine Equations
Objectives
By the end of this module, students will be able to:
Understand and solve Diophantine equations.
Assignments
Read Module 31
Complete the Problem Set for Module 31.
Introduction
Diophantine
MATH 116
Prof. Houston
Module 24
Linear Equations Modern Methods
Objectives
By the end of this module, students will be able to:
Solve linear equations in one variable using modern methods (review).
Assignments
Read Module 24
Read MTTA Sketch 8, "The Coss
Explanation of Example (2) on P. 7 of Module 29
So we are starting with the following system of equations:
4 x 3y 22
4 x 5 y 6
Step 1: Write the augmented matrix of the system of linear equations.
As shown by example in the module, the augmented matrix fo
College Algebra and Trigonometry
a.k.a. Precalculus
by
Carl Stitz, Ph.D.
Lakeland Community College
Jeff Zeager, Ph.D.
Lorain County Community College
August 30, 2010
ii
Acknowledgements
The authors are indebted to the many people who support this project
Westchester Community College
Math 135 College Algebra with Trigonometry - 81922
Fall 2016 TTh 11:00am-12:50pm Tech 107
Instructor: Matthew Rogala
Office Hours: M 12-1pm, 5-6pm, T 4-5pm,
Office: Tech 145A (Tel: 914-606-6524)
W 5-6pm, Th 10-11am
Email: Mat
experience suggests that many students misunderstand these terms. Teaching tip:
Wikipedia (www.wikipedia.org) has a good summary and some links for more
information on Kristen Gilbert.
Homework Activities
5
1
Activity 1-1
In this topic, the homework activ
SECTION 2.2
STATISTICAL INFERENCE
FROM SAMPLE TO
POPULATION
BIG IDEA OF THE DAY
Chapter 1 sampling from a process
Observing
a small number of attempts from an
infinite number of possible attempts.
Buzz and Doris do the experiment forever.
Chapter 2 samp
Investigation Chapter 1: Tire Story Falls Flat
PART I
A legendary story on college campuses concerns two students who miss a chemistry exam
because of excessive partying but blame their absence on a flat tire. The professor allows them
to take a make-up e
Investigation Chapter 1: Tire Story Falls Flat
PART I
A legendary story on college campuses concerns two students who miss a chemistry exam
because of excessive partying but blame their absence on a flat tire. The professor allows them
to take a make-up e
Chapter 2 Modeling with Linear Functions
Section 2.1 Using Lines to Model Data
Scattergram: a graph of plotted ordered pairs. It should have scaling on both
axes and labels indicating the variable names and scale units.
We will use qualitative graphs to d