1. Modeling Discrete Variables
Lecture 27
Section 6.4
Wed, Mar 3, 2004

2. Discrete Distributions
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.

3. Example: Lotto South
Let X be the winning value of a Lotto South ticket.
See

4. Example: Lotto South The possible values of X are
$ (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)

5. Example: Lotto South Winning Value Proportion of Tickets $2,000,000
$1,000
$75 $5
0.0175 $0
0.981

6. Proportion of Households
Example
Let X be the number of cars owned by a household.
Number of Cars
Proportion of Households
0.10 1
0.30 2
0.35 3
0.15 4

7. Graph of a Discrete Distribution
A spike graph:
0.40
0.30
Proportion of Households
0.20
0.10
0.00 1 2 3 4
Number of Cars

8. Graph of a Discrete Distribution
What proportion of households own at least 2 cars?
0.40
0.30
Proportion of Households
0.20
0.10
0.00 1 2 3 4
Number of Cars

9. Graph of a Discrete Distribution
What proportion of households own at least 2 cars?
0.40
0.30
Proportion of Households
0.20
0.10
0.00 1 2 3 4
Number of Cars

10. Graph of a Discrete Distribution
What proportion of households own at least 2 cars?
0.40
0.35
0.30
Proportion of Households
0.20
0.15
0.10
0.00 1 2 3 4
Number of Cars

11. Graph of a Discrete Distribution
The proportion is = 0.60.

12. Discrete Distributions
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.

13. Discrete Distributions
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.
Binomial.
Geometric.
Hypergeometric.
Poisson.

14. Assignment
Page 358: Exercises 42 – 46.