STAT 430/510 Lecture 7
STAT 430/510 Probability
Hui Nie
Lecture 7
June 4th, 2009
This
preview
has intentionally blurred sections.
Sign up to view the full version.
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.
This
preview
has intentionally blurred sections.
Sign up to view the full version.
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
This
preview
has intentionally blurred sections.
Sign up to view the full version.
STAT 430/510 Lecture 7
Example
Three balls are to be randomly selected without
This is the end of the preview.
Sign up
to
access the rest of the document.
- Summer '08
- KRIEGER
- Conditional Probability, Probability, Probability theory, Hui Nie
-
Click to edit the document details
