Modeling Discrete Variables

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Presentation transcript:

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

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.

Example: Lotto South Let X be the winning value of a Lotto South ticket. See http://www.valottery.com/lottosouth/howtoplay.asp

Example: Lotto South 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)

Example: Lotto South Winning Value Proportion of Tickets $2,000,000 0.0000000715 $1,000 0.0000184 $75 0.000969 $5 0.0175 $0 0.981

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

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

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

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

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

Graph of a Discrete Distribution The proportion is 0.35 + 0.15 + 0.10 = 0.60.

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.

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.

Assignment Page 358: Exercises 42 – 46.