Transcript Lecture 27 - Modeling Discrete Variables

Modeling Discrete
Variables
Lecture 27
Section 6.4
Wed, Mar 3, 2004
Discrete Distributions
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If X is a discrete variable, then it can
equal only specific values.
We will assume that there are only a
finite number of possible values.
Therefore, we can list the possible
values of X along with the proportion
of the population with that value.
Example: Lotto South
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Let X be the winning value of a Lotto
South ticket.
See
http://www.valottery.com/lottosouth/howtoplay.asp
Example: Lotto South
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The possible values of X are
$2000000 (1 out of 13,983,816)
 $1000 (1 out of 54,201)
 $75 (1 out of 1,032)
 $5 (1 out of 57)
 $0 (whatever is left)
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Example: Lotto South
Winning Value
$2,000,000
Proportion of Tickets
0.0000000715
$1,000
0.0000184
$75
0.000969
$5
0.0175
$0
0.981
Example
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Let X be the number of cars owned by
a household.
Number of Cars
Proportion of Households
0
0.10
1
0.30
2
0.35
3
0.15
4
0.10
Graph of a Discrete
Distribution
A spike graph:
Proportion of Households
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0.40
0.30
0.20
0.10
0.00
0
1
2
Number of Cars
3
4
Graph of a Discrete
Distribution
What proportion of households own at
least 2 cars?
Proportion of Households

0.40
0.30
0.20
0.10
0.00
0
1
2
Number of Cars
3
4
Graph of a Discrete
Distribution
What proportion of households own at
least 2 cars?
Proportion of Households

0.40
0.30
0.20
0.10
0.00
0
1
2
Number of Cars
3
4
Graph of a Discrete
Distribution
What proportion of households own at
least 2 cars?
Proportion of Households

0.40
0.35
0.30
0.20
0.15
0.10
0.00
0
1
2
Number of Cars
3
4
Graph of a Discrete
Distribution
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The proportion is 0.35 + 0.15 + 0.10
= 0.60.
Discrete Distributions
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Discrete distributions are simple in the
sense that we just add up numbers
(no areas to calculate).
On the other hand, there may be no
simple way to describe the distribution
other than to write a long table of
numbers.
Discrete Distributions
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It would be very convenient if there were a
formula we could use to calculate the
proportion for each value of X.
In fact, there are a number of such
formulas, designed for special situations.
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Binomial.
Geometric.
Hypergeometric.
Poisson.
Assignment
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Page 358: Exercises 42 – 46.