This preview shows pages 1–2. Sign up to view the full content.
MA/STAT416: Probability
Lecture Notes
Spring 2011 1
Chapter 4: Discrete Random Variables and Mass Functions
February 18, 2011
4.1
Mass Function and Mode of a Random Variable
Deﬁnition 1.
The mode is the most probable value; the value with the highest proba
bility.
Deﬁnition 2.
Let
X
be a discrete random variable taking the values
x
1
,x
2
,
···
. The
probability mass function of
X
is deﬁned by
p
(
x
) =
P
(
X
=
x
), where
x
=
x
1
,x
2
,
···
.
Note
p
(
x
) = 0 otherwise.
4.2
CDF and Median of a Random Variable
Deﬁnition 3.
The cumulative distribution function CDF of a random variable
X
is the
function
F
(
x
) =
P
(
X
≤
x
).
Deﬁnition 4.
Given the CDF
F
(
x
) for
X
. Any number
m
such that
P
(
X
≤
m
)
≥
0
.
5
and
P
(
X
≥
m
)
≥
0
.
5 is called a median of
X
. The median is not unique.
4.3
Examples
Example
5
.
A fair coin is tossed twice. Let
X
be the number of heads. Find the pmf of
X
.
Example
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview. Sign up
to
access the rest of the document.
This note was uploaded on 04/23/2011 for the course STAT 416 taught by Professor Staff during the Spring '08 term at Purdue UniversityWest Lafayette.
 Spring '08
 Staff
 Probability

Click to edit the document details