ST371
Introduction to Proabability
and Distribution Theory
Continuous Random Variables
Gamma Models
Page 1
ST371-15 cont rv 03
(c) Tom Gerig
The (Complete) Gamma Function
The (Complete) Gamma Function
The complete gamma function is defined as:
complete ga
ST371
Tom Gerig 1
ST371
Midterm Examination I
May 31, 2007
Closed books and notes. You may use one page of notes (8 by 11, both
sides, any content). You will need a calculator.
NAME: _
Row #: _
Before you turn in your examination, please sign and date bel
ST371
Tom Gerig 1
ST371
Midterm Examination I
June 1, 2006
Closed books and notes. You may use one page of notes (8 by 11, both
sides, any content). You will need a calculator.
NAME: _
Row #: _
Before you turn in your examination, please sign and date bel
ST371
Tom Gerig 1
ST371
Midterm Examination I
February 9, 2005
Closed book and notes. You may use one sheet of notes (8 by 11, both sides).
You will need a calculator.
NAME: _
Row #: _
Before you turn in your examination, please acknowledge that you have
ST371
Tom Gerig 1
ST371
Midterm Examination I
June 10, 2004
Closed book and notes. You may use one sheet of notes (81/2 by 11, both sides).
You will need a calculator.
NAME: _
Row #: _
Before you turn in your examination, please sign and date the followin
ST371
Tom Gerig 1
ST371
Midterm Examination I
June 4, 2003
Closed book and notes. You may use one sheet of notes (81/2 by 11, both
sides). You will need a calculator.
NAME: _
Column #: _
Before you turn in your examination, please sign and date the follow
ST371
Introduction to Probability and
Distribution Theory
Distributions of Functions of
Random Variables
Method of Transformations
Page 1
ST371-xx
(c) Tom Gerig
Method of Transformations
Let Y be a rv with pdf fY ( y ). Let h( y ) be a
(strictly) increasi
ST371
Introduction to Probability and
Distribution Theory
Central Limit Theorem
(c) Tom Gerig
ST371-22 fns of rv 02
1
Central Limit Theorem
Assume that X 1 , . , X n are iidrv with mean
and variance . Suppose that . Then
as n increases to the distributio
ST371
Introduction to Probability and
Distribution Theory
Joint Probability Distributions:
Linear Combinations
Page 1
ST371-21 fns of rv 01
(c) Tom Gerig
Linear Combinations
Let X 1 , X 2 , ., X n be n rvs and a1 , a2 , . an be
n numerical constants. Then
ST371
Distribution Theory
Introduction to Probability and
Joint Probability Distributions:
Multinomial Distribution
Page 1
ST371-20 joint rv 04
(c) Tom Gerig
Multinomial Experiment
The following structure defines a Multinomial
Experiment:
n indentical an
ST371
Introduction to Probability and
Distribution Theory
Joint Probability Distributions:
Covariance and Correlation
Page 1
ST371-19 joint rv 03
(c) Tom Gerig
Expectation of a Function of ( X , Y )
Let ( X , Y ) be discrete random variables with
joint pr
ST371
Introduction to Probability and
Distribution Theory
Continuous Random Variables
Joint Probability Distributions
Page 1
ST371-18 joint rv 02
(c) Tom Gerig
Outline
Continuous random variables:
Joint pdf of ( X , Y )
Marginal distribution (pdf ) of X
C
ST371
Introduction to Probability and
Distribution Theory
Discrete Random Variables
Joint Probability Distributions
Page 1
ST371-17 joint rv 01
(c) Tom Gerig
Outline
Discrete random variables:
Joint pmf of ( X , Y )
Marginal distribution (pmf ) of X
Condi
ST371
Tom Gerig 1
ST371
Midterm Examination I
May 29, 2008
Closed books and notes. You may use one page of notes (8 by 11, both
sides, any content). You will need a calculator.
NAME: _
Row #: _
Before you turn in your examination, please sign and date bel