STA 711: Probability & Measure Theory
Robert L. Wolpert
2
Construction & Extension of Measures
For any finite set = cfw_1 , ., n , the power set P() is the collection of all subsets of
, including the
STA 711: Probability & Measure Theory
Robert L. Wolpert
3 Random Variables & Distributions
Let
be any set, F any -eld on
, and P any probability measure dened for eah element
of F ; suh a triple (
STA 711: Probability & Measure Theory
Robert L. Wolpert
5 Expetation Inequalities and Lp Spaes
Fix a probability spae (
; F ; P) and, for any real number p > 0 (not neessarily an integer)
and let \Lp"
STA 711: Probability & Measure Theory
Robert L. Wolpert
6 Independene
6.1 Independent Events
A olletion of events fA g F in a probability spae (
; F ; P) is alled independent if
i
P [\i2I Ai =
Y
2
P[A
Midterm Examination I
STA 711: Probability & Measure Theory
Wednesday, 2016 Ot 05, 1:25 cfw_ 2:40pm
This is a losed-book exam. You may use a single sheet of
prepared notes, if you wish, but you may no
STA 711: Probability & Measure Theory
Robert L. Wolpert
4 Expetation & the Lebesgue Theorems
Let X and fXn : n 2 N g be random variables on the same probability spae (
; F ; P). If
Xn (! ) ! X (! ) fo
Midterm Examination I
STA 711: Probability & Measure Theory
Wednesday, 2014 Ot 1, 1:25 cfw_ 2:40pm
This is a losed-book exam. You may use a single sheet of
prepared notes, if you wish, but you may not
STA 711: Probability & Measure Theory
Robert L. Wolpert
7 Convergene in R d and in Metri Spaes
A sequene of elements an of R d onverges to a limit a if and only if, for eah > 0, the
sequene an eventua
STA 711: Probability & Measure Theory
Robert L. Wolpert
Housekeeping Details
Introduction
Lec: Mon/Wed 1:252:40pm, in 126 Sociology/Psychology Building (moved from 124
Social Sciences to larger room
Midterm Examination I
STA 711: Probability & Measure Theory
Wednesday, 2015 Sep 30, 1:25 2:40pm
This is a closed-book exam. You may use a single sheet of
prepared notes, if you wish, but you may not s