9/18/2014
www4.stat.ncsu.edu/~bmasmith/ST371S11/sg2NOW.html
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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 (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 (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 (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
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 (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
HW12
3
4 (parts a and e* only)
20 (part a only; calculate both the large sample confidence interval and the score interval)
37 (part a only)
Homework Page 1
1) Use the summary measures from problem 10.5 to create an ANOVA table (note: the pvalue for the factor of interest
is 0.196); also draw a welllabeled picture of the pvalue.
2) Consider the information presented in problem 10.27. Use the summary statis
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
www4.stat.ncsu.edu/~bmasmith/ST371S11/sgq1.html
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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
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
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
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
9/18/2014
www4.stat.ncsu.edu/~bmasmith/ST371S11/syllabus.html
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SPRING
2011
STATISTICS
S3102
T70
I s r c o :D . C E S i h 4 4 S S H l , P o e 5 5 1 0 ,
n t u t r r . . mt, 28 A al hn 197
Ofc Hus TA(o
HW3
Sunday, February 5, 2017
12:18 PM
5 (Note: the pvalue for the factor of interest is 0.104)
17 (part a only); a partially completed ANOVA table for this problem is:
DF
SS
MS
F
pvalue
Sand
0.065
Fiber
0.016
Interaction
0.585
Error
Total
19; a parti
Homework 4
Problem 1 (based off of 10.5)
From the information provided, . . = 1.5367
Source
Treatment
Error
Total
DF
2
27
29
SS
0.2286
1.782
MS
0.1143
0.0660
Fstatistics
1.73
pvalue
0.196
MS
7.83
2.09
Fstatistics
3.75
pvalue
0.028
F2,27 distribution
p
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
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
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
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
HW9
Chapter 2: Problem 45
Chapter 3: Problem 32
Chapter 4: Problem 15 (note: for part a, you do not need to graph the pdf or cdf)
Homework Page 1
Homework Page 2
HW2
Wednesday, January 25, 2017
9:33 AM
4 (Note: pvalue = 0.218)
7 (Note: pvalue is basically 0, but you shouldn't need me to tell you that!
24 (Note: pvalue = 0.003); for the multiple comparisons part, use the following information to help you dete
HW1
Saturday, January 14, 2017
1:53 PM
1) Complete problem 5 in Chapter 1 of the textbook
2) For the populations described in problem 1 (in Chapter 1) parts (b) and (c):
(a) Describe how you would take a simple random sample of the population
(b) Describe