ST371 (I). Basics of Probability
1
What is Probability
Much of what occurs in life involves situations where we are uncertain about
what is going to happen. Probability is a mathematical model for quantifying the uncertainty in these situations. It is the
ST 371 (VI): Continuous Random Variables
So far we have considered discrete random variables that can take on a
ﬁnite or countably inﬁnite number of values. In applications, we are often
interested in random variables that can take on an uncountable conti
ST 371 (III). Conditional Probability and
Independence
1
Conditional Probability
In this section, we are interested in answering this type of question: how the
information “an event B has occurred” aﬀects the probability that “ event
A occurs”.
Reallife
ST 371 (VII): Families of Continuous
Distributions
1
Normal Distribution
The family of normal random variables plays a central role in probability
and statistics. This distribution is also called the Gaussian distribution
after Carl Friedrich Gauss, who p
ST 371 (IV): Discrete Random Variables
1
Random Variables
A random variable (rv) is a function that is deﬁned on the sample space of
the experiment and that assigns a numerical variable to each possible outcome of the experiment. We denote random variable
ST 371 (VIII): Theory of Joint Distributions
So far we have focused on probability distributions for single random variables. However, we are often interested in probability statements concerning
two or more random variables. The following examples are il
ST 371 (IX): Theories of Sampling
Distributions
1
Sample, Population, Parameter and Statistic
The major use of inferential statistics is to use information from a sample
to infer characteristics about a population.
A population is the complete collection
9/18/2014
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Morgan Carter
February 1, 2011
ST37102
Professor Smith
Class Summary
Review from last session:
n
n!
=
n = n1 + n 2 + .+ n k
n1,n 2 .n k n1!n 2!.n k! where
This can be used for the # of ways to rearrange
Brent Clayton
Homework #0
Summary of class notes 2/3/2011
The lecture notes for this particular day a centered on sections 2.42.5 in the Devore book.
Basically the idea of conditional probability is presented here. Conditional probability states
that giv
Joel Anderson
ST 371002
Lecture Summary for 2/15/2011
Homework 0
First, the definition of a probability mass function p(x) and a cumulative distribution function
F(x) is reviewed:
Graphically, the drawings of a pmf and a cdf (regarding discrete random va
The lecture on 2/8/2011 mainly focused on independence.
Two events A and B are independent if P(AB)=P(A) and are dependent otherwise.
If two events are independent then they cannot be mutually exclusive.
Reliability: Parallel= 1(1P(A)*(1P(A2)*.(1P(An
9/18/2014
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ST 371 (V): Families of Discrete
Distributions
Certain experiments and associated random variables can be grouped
into families, where all random variables in the family share a certain structure and a particular random variable in the family is described
ST 371 (II). Calculating Probabilities
1
Sample Spaces Having Equally Likely Outcomes
For many experiments, it is natural to assume that all outcomes in the
sample space are equally likely to occur. That is, consider an experiment
whose sample space S is
9/18/2014
HOMEWORK ASSIGNMENTS Smith Section ST 371
HOMEWORK and READING ASSIGNMENTS
for ST371002 Smith Section SPRING 2011
WEEK 1 Readings: Cartoon Guide Chapters 1 and 2
Devore: Chapter 1
URL for football data
HW # 1 Due Thursday Jan 27, 2011
1. journa
9/18/2014
HOMEWORK ASSIGNMENTS Smith Section ST 371
HOMEWORK and READING ASSIGNMENTS
for ST371002 Smith Section Spring 2011
HW # 2 Due Tuesday Feb 8, 2011
Last 2 problems are in Devore.
1. How many distinguishable ways can the word
HUMUHUMUNUKUNUKUAPUAA
HW 3 solutions:
Problem 1: The table below shows the number of students that fall into each of several
categories. One student will be selected at random in a raffle, and will be given a new laptop PC
with a PEEP screensaver on it.
FEMALE
CE
FEMALE
EE
FEM
Problem 8: text p 76 # 68
Define events A1, A2, and A3 as flying with airline 1, 2, and 3, respectively. Events 0, 1, and 2 are 0, 1, and 2 flights
are late, respectively. Event DC = the event that the flight to DC is late, and event LA = the event that t
ST 371 Spring 2011
1. p 155 # 36
2. p 155 # 44
3. p 156 # 50
4. p156 # 54
5. p. 162 # 60
6. p. 162 # 66
7. p. 168 # 72
8. p. 169 # 76
9. p. 169 # 82
10. p. 169 # 84
HW 6 due March 29
HW 3 ST 371 Spring 2011 Due Feb. 15, 2011
Problem 1: The table below shows the number of students that fall into each of several
categories. One student will be selected at random in a raffle, and will be given a new laptop PC
with a PEEP screensaver on i
Hw4duefeb22,2011
reading: chapter 3 in Devore
1. p. 90 # 10
1.
a.
T = total number of pumps in use at both stations. Possible values: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10
b. X: 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 6
c.
U: 0, 1, 2, 3, 4, 5, 6
d. Z: 0, 1, 2
2. p.