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07-W4959 10/7/08 3:06 PM Page 359
7.1
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Random Variables 359
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Example 7.1
Car Sales
Consider an experiment in which the type of car, new (N) or used (U), chosen by
each of three successive customers at a discount car dealership is noted. Define a
random variable x by
x number of customers purchasing a new car
The experimental outcome in which the first and third customers purchase a new car
and the second customer purchases a used car can be abbreviated NUN. The associated x value is 2, because two of the three customers selected a new car. Similarly,
the x value for the outcome NNN (all three purchase a new car) is 3. We display
each of the eight possible experimental outcomes and the corresponding value of x
in the following table:
Outcome UUU NUU UNU UUN
NNU NUN
UNN
NNN
x value
0
1
1
1
2
2
2
3
There are only four possible x values—0, 1, 2, and 3—and these are isolated points
on the number line. Thus, x is a discrete random variable.
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In some situations, the random variable of interest is discrete, but the number of
possible values is not finite. This is illustrated in Example 7.2.
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Example 7.2
This Could Be a Long Game . . .
Two friends agree to play a game that consists of a sequence of trials. The game
continues until one player wins two trials in a row. One random variable of interest
might be
x number of trials required to complete the game
Let A denote a win for Player 1 and B denote a win for Player 2. The simplest possible experimental outcomes are AA (the case in which Player 1 wins the first two
trials and the game ends) and BB (the case in which Player 2 wins the first two trials). With either of these two outcomes, x 2. There are also two outcomes for which
x 3: ABB and BAA. Some other possible outcomes and associated x values are
Outcomes
AA, BB
BAA, ABB
ABAA, BABB
ABABB, BABAA
o
ABABABABAA, BABABABABB
and so on.
x value
2
3
4
5
o
10