Math 5p87
Lecture 12
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 13, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Theorem 13.5: approximating gener
Math 5p87
Lecture 16
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 6, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Review of Distributions
is the distr
Math 5p87
Lecture 14
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 27, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Proof of MCT
Proving (iii) 0 Xn X
Math 5p87
Lecture 11
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 11, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Revisiting the independence of fu
Math 5p87
Lecture 13
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 25, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Expectation (integration)
(, F ,
Math 5p87
Lecture 15
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 4, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
(, F , P) vs (R, R, )
rvs are dened b
Math 5p87
Lecture 17
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 11, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Creating more distributions
Based on
Math 5p87
Lecture 21
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 25, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Betting system
The gamblers ruin is
Math 5p87
Lecture 22
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 25, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Tree diagram and elementary conditio
Math 5p87
Lecture 20
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 20, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Gambling and gamblers ruin
iid cfw_X
Math 5p87
Lecture 18
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 13, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Proof of Theorem 20.4
Theorem 20.4.
Math 5p87
Lecture 19
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
March 18, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Veriable conditions for as
Recall th
Math 5p87
Lecture 7
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 28, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Proof of Theorem 4.1.(a)
Theorem 4.
Math 5p87
Lecture 1
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 7, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Introduction
Perform an experiment.
Math 5p87
Lecture 6
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 28, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Independent classes (nite case)
Cla
Math 5p87
Lecture 2
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 9, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
The easiest uncountable example
We a
Math 5p87
Lecture 8
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 30, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Some more coin ipping examples
1
2
a
. -- l _' ' '4' n
; _|..{ l . Y 1} " _ JJ. . . L
I
I . ' i. . _ J [ .
i , t . k x I .. .
\' ,' , I . a .- r '
Li h "a L w: ~ '
J
' ~I J3C 'r l};
. | '
! u I" fA IS -.'\ {1 J, l I l
. -. a w
Math 5p87
Lecture 3
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 14, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Equivalence relation
A relation on
Math 5p87
Lecture 4
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 16, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Probability triple
F P() is a -eld
Math 5p87
Lecture 9
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 4, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Role of -system
P is a -system if A
Math 5p87
Lecture 10
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
February 6, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
More on simple rvs
(, F , P). X :
Math 5p87
Lecture 5
Wai Kong (John) Yuen
[email protected]
Department of Mathematics, Brock University
January 21, 2014
Wai Kong (John) Yuen [email protected]
Math 5p87
Last thing to check for (0, 1], B,