Covariance, Expectation of Linear Combinations, & Conditional Expectation
1 Covariance
1.1 Motivation
While the joint PDF of two random variables fully describes the relationship between two random v
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Chapter 4.2-4.9
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4.2 The Probability Distribution for a Continuous Random Variable
4.2 The Probability Distribution for
STAT 3375 Review of Calculus and Some Basic Concepts
1 Dierentiation
1.1 Denitions
Let f be a function which is dened on some interval (c, d) and let a be some number in this interval. The
derivative
Outline 6.3 The Method of Distribution Functions 6.4 The Method of Transformations 6.5 The Method of Moment-Generatin
STAT 3375Q
6.3 6.5
December 2, 2014
STAT 3375Q 6.3 6.5
Outline 6.3 The Method of D
Review List
1. The nal Exam will have 6 problems. There are no true or false questions. The only two
proofs are from the list in the end. Another two problems are from the homework.
2. You are allowed
Outline
6.7 Order Statistics
STAT 3375Q
6.7 Order Statistics
August 18, 2014
STAT 3375Q 6.7 Order Statistics
Outline
6.7 Order Statistics
1 6.7 Order Statistics
STAT 3375Q 6.7 Order Statistics
Outline
Outline
5.8 The Expected Value and Variance of Linear Functions of Random Variables
STAT 3375Q
5.8 and 5.11
August 18, 2014
STAT 3375Q 5.8 and 5.11
5.11 Conditional Expectations
Outline
5.8 The Expect
Outline
5.3 Marginal and Conditional Probability Distributions
STAT 3375Q
5.3-5.4
August 18, 2014
STAT 3375Q 5.3-5.4
5.4 Independent Random Variables
Outline
5.3 Marginal and Conditional Probability D
Outline
5.2 Bivariate and Multivariate Probability Distributions
STAT 3375Q
5.2
STAT 3375Q 5.2
Outline
5.2 Bivariate and Multivariate Probability Distributions
1 5.2 Bivariate and Multivariate Probabi
Outline
5.5 The Expected Value of a Function of Random Variables
STAT 3375Q
5.5-5.6
August 18, 2014
STAT 3375Q 5.5-5.6
5.6 Special Theorems
Outline
5.5 The Expected Value of a Function of Random Varia
Outline
5.7 The Covariance of Two Random Variables
STAT 3375Q
5.7
August 18, 2014
STAT 3375Q 5.7
Outline
5.7 The Covariance of Two Random Variables
1 5.7 The Covariance of Two Random Variables
5.7 The
Outline
4.7 The Beta Probability Distribution
STAT 3375Q
4.7-4.9
August 18, 2014
STAT 3375Q 4.7-4.9
4.9 Other Expected Values
Outline
4.7 The Beta Probability Distribution
1 4.7 The Beta Probability D
STAT 3375Q
4.6
October 16, 2014
STAT 3375Q 4.6
October 16, 2014
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4.6 The Gamma Probability Distribution
STAT 3375Q 4.6
October 16, 2014
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4.6 The Gamma Probability Distribution
The gamma
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Chapter 2
September 8, 2014
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September 8, 2014
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2.3 A Review of Set Notation
Set Theory
Symbol
Denition
Union
Intersection
is an element of
is not an element of
Nu
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Chapter 3.7-3.9
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STAT 3375Q Chapter 3.7-3.9
September 25, 2014
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Section 3.7 - 3.9
3.7 The Hypergeometric Probability Distribution
3.8 Poisson Probability Distribut
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Chapter 2
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September 16, 2014
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Chapter 2
2.7 Conditional Probability and the Independence of Events
2.8: Two Laws of Probability
2.9 Calculati
Outline
3.4 The Binomial Probability Distribution
STAT 3375Q
Chapter 3.4
August 18, 2014
STAT 3375Q Chapter 3.4
Outline
3.4 The Binomial Probability Distribution
1 3.4 The Binomial Probability Distrib
STAT 3375 Review
1 Taylor Series
1.1 Denition
Let f be a function which is dened and innately dierentiable at all points on some interval (c, d) and let
a be some number in this interval. If f is anal
1
Set Theory Denitions
A set is simply a collection of objects:
The set of counting numbers
The set of students in this classroom
The set of professors in the statistics department
Typical notati
1
Probability Experiments
Experiments
A probability experiement is an activity that involves chance that
leads to results, that can be repeated
Sample Points
A Sample point is a possible result of
Indepence & Expectation
1 Indepence
1.1 Motivation
Much like how we discussed the concept of two events being independent of each
other, we can also discuss the idea of random variables being indepen
Marginal & Conditional Distributions
1 Motivation
We began this section of the course discussing the situation in which we take
multiple measurements at the same time and would like to model how the
Multivariate Distributions
1 Motivation
Often when we are studying a particular topic we will take various measures that
pertain to that topic
From hre the goal is usually to examine these measures
The Gamma Distirbution
1 Denition & Motivation
Our last continuous Distribution is the Beta distribution
The Beta distribution is very useful for modeling bounded random variables with
a non uniform
The Gamma Distirbution
1 Denition & Motivation
Often times we would like to model a continuous Random variable that only has
a positive support
In these cases, the Normal distribution is not an appr
The Normal Distribution
1 Denition & Motivation
Known by several names including Normal, Gaussian, Bell curve/distribution (here
we will call it the Normal distirbution), the Normal distribution is p
The Gamma Function
1 Denition
Here we will go over the Gamma Function, a function used to verify the Gamma
distribution and the Normal distribution.
Denition 1. The Gamma Function is the function (de
Continuous Uniform Random Variables
1 Motivation & Denition
We will begin to examine various Continuous Random variables, and we will start
with one of the Simplest, the continuous Uniform Random Var
Continuous Random Variables
1 Denition
Now that we have discussed Discrete Random Variables we will now move on to
continuous Random Variables
Like Discrete Random Variables, continuous Random Varia