Lecturenotes7 - STAT 430/510 Lecture 7 STAT 430/510...

STAT 430/510 Lecture 7
STAT 430/510 Probability
Hui Nie
Lecture 7
June 4th, 2009

STAT 430/510 Lecture 7
Review
Properties of Probability
Conditional Probability
The Law of Total Probability
Bayes Formula
Independence

STAT 430/510 Lecture 7
Random Variables
In most problems, we are interested only in a particular
aspect of the outcomes of experiments.
Example: When we toss 10 coins, we are interested in the
total number of heads, and not the outcome for each coin.

STAT 430/510 Lecture 7
Definition
For a given sample space S , a random variable (r.v.) is a
real-valued function defined over the elements of S .

STAT 430/510 Lecture 7
Example
Suppose that our experiment consists of tossing 3 fair
coins. If we let Y denote the number of heads that appear,
then Y is a random variable taking on one of the values
0,1,2 and 3 with respective probabilities
P { Y = 0 } = P { ( T , T , T ) } =
1
8
P { Y = 1 } = P { ( T , T , H ) , ( T , H , T ) , ( H , T , T ) } =
3
8
P { Y = 2 } = P { ( T , H , H ) , ( H , T , H ) , ( H , H , T ) } =
3
8
P { Y = 3 } = P { ( H , H , H ) } =
1
8