This preview shows pages 1–3. Sign up to view the full content.
Chapter 3: Random Variables and Probability Distributions
45
CHAPTER 3 — RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
A
random variable
is a function that associates a real number with each element of a sample
space.
•
A random variable is generally denoted by a capital letter:
X, Y,
etc.
•
An observed value of a random variable is denoted by a lowercase letter:
x, y,
etc.
Example:
Suppose a coin is flipped 3 times.
The sample space is for this experiment is
{ }
TTT
HTT
THT
TTH
THH
HTH
HHT
HHH
S
,
,
,
,
,
,
,
=
.
Letting
X
be the random variable describing the number of heads observed, we obtain:
Sample Space
Elements
x
HHH
3
HHT, HTH, THH
2
HTT, THT, TTH
1
TTT
0
Example
:
Suppose an individual plays the lottery each week until he wins the jackpot (and then
he stops).
Letting
W
represent the event that the individual wins the lottery, and letting
L
represent the event that the individual does not win, our sample space is:
{ }
K
,
,
,
,
,
LLLLW
LLLW
LLW
LW
W
S
=
We may construct a random variable,
X
, to indicate the number of weeks it takes the individual
to win the lottery:
Sample Space
Elements
x
W
1
LW
2
LLW
3
LLLW
4
LLLLW
5
M
M
In each of the above examples, the set of possible values of
X
is discrete.
Such random variables
are called
discrete random variables
.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentChapter 3: Random Variables and Probability Distributions
46
Random variables with an uncountable number of possible values are called
continuous
random
variables
.
Example
:
Doug arrives at his bus stop and records the time (in minutes) until his bus arrives.
Let
X
be the random variable representing this time.
The sample space is
This is the end of the preview. Sign up
to
access the rest of the document.
 Spring '08
 Noe
 Statistics, Probability

Click to edit the document details