Lecture_1-2_July_2010 - EE 131A Probability Professor Kung...

UCLA EE131A (KY) 1
EE 131A Probability
Professor Kung Yao
Electrical Engineering Department
University of California, Los Angeles
M.S. On-Line Engineering Program
Lecture 1-2

UCLA EE131A (KY) 2
Set theory (1)
• In probability, we deal with probability of events.
• Often, we have to deal with various operations on
these events and then evaluate their probabilities.
• However, events are sets in mathematics.
• Thus, operations involving events require various set
operations.
• While most you have had set theory before, we will
introduce, define, and review these concepts fully in
the next few vu graphs.

UCLA EE131A (KY) 3
Set theory (2)
• Union of set A and set B , denoted by A  B , consists
of elements in A and as well as in B .
• Symbolically, if A is denoted by the elliptical figure
and B is denoted by the rectangular figure, then
A  B is denoted by the darkened figure
• Ex. 1. A = {1,2} and B = {3,4}. Then A  B = {1,2,3,4}.
• Ex. 2. A = {1,2,3} and B = {3,4}. Then A  B = {1,2,3,4}.
Note: In Ex. 2, we do not write A  B = {1,2,3,3,4}.