Probability primer
1/08/13
Probability Primer
Principles of Econometrics, 4th Edition
Probability Primer
Page 1
! Announcement:
! Please make sure you know who your tutor is and remember their names. This will save confusion and embarrassment later.
! Kai Du (David)
! Ngoc Thien Anh Pham (Anh)
! Zara Bomi Shroff
Principles of Econometrics, 4th Edition
Probability Primer
Page 2
Chapter Contents
¡ P.1 Random Variables
¡ P.2 Probability Distributions
¡ P.3 Joint, Marginal and Conditional Distributions
¡ P.4 A Digression: Summation Notation
¡ P.5 Properties of Probability Distributions
¡ P.6 The Normal Distribution
Principles of Econometrics, 4th Edition
Probability Primer
Page 3
1
1/08/13
P.1
Random Variables
Principles of Econometrics, 4th Edition
Probability Primer
Page 4
P.1
Random Variables
! A random variable is a variable whose value is unknown until it is observed; in other words it is a variable that is not perfectly predictable
– Each random variable has a set of possible values it can take
– A discrete random variable can take only a limited, or countable, number of values
• An indicator variable taking the values one if yes, or zero if no
• Indicator variables are discrete and are used to represent qualitative characteristics such as gender (male or female), or race (white or nonwhite) – A random variable that can have any value is treated as a continuous random variable
Principles of Econometrics, 4th Edition
Probability Primer
Page 5
P.2
Probability Distributions
Principles of Econometrics, 4th Edition
Probability Primer
Page 6
2
1/08/13
P.2
Probability
Distributions
! Probability is usually defined in terms of experiments – If we were to select one cell from the table at random, that would constitute a random experiment Principles of Econometrics, 4th Edition
P.2
Probability
Probability Primer
Principles of Econometrics, 4th Edition
Probability Primer
Page 1
! Announcement:
! Please make sure you know who your tutor is and remember their names. This will save confusion and embarrassment later.
! Kai Du (David)
! Ngoc Thien Anh Pham (Anh)
! Zara Bomi Shroff
Principles of Econometrics, 4th Edition
Probability Primer
Page 2
Chapter Contents
¡ P.1 Random Variables
¡ P.2 Probability Distributions
¡ P.3 Joint, Marginal and Conditional Distributions
¡ P.4 A Digression: Summation Notation
¡ P.5 Properties of Probability Distributions
¡ P.6 The Normal Distribution
Principles of Econometrics, 4th Edition
Probability Primer
Page 3
1
1/08/13
P.1
Random Variables
Principles of Econometrics, 4th Edition
Probability Primer
Page 4
P.1
Random Variables
! A random variable is a variable whose value is unknown until it is observed; in other words it is a variable that is not perfectly predictable
– Each random variable has a set of possible values it can take
– A discrete random variable can take only a limited, or countable, number of values
• An indicator variable taking the values one if yes, or zero if no
• Indicator variables are discrete and are used to represent qualitative characteristics such as gender (male or female), or race (white or nonwhite) – A random variable that can have any value is treated as a continuous random variable
Principles of Econometrics, 4th Edition
Probability Primer
Page 5
P.2
Probability Distributions
Principles of Econometrics, 4th Edition
Probability Primer
Page 6
2
1/08/13
P.2
Probability
Distributions
! Probability is usually defined in terms of experiments – If we were to select one cell from the table at random, that would constitute a random experiment Principles of Econometrics, 4th Edition
P.2
Probability