# Discrete Probability Distributions

5. To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.

A. List the experimental outcomes associated with performing the blood analysis.

B. If the random variable of interest is the total number of steps required to do the complete analysis (both procedures), show what value the random variable will assume for each of the experimental outcomes?

9. Nationally, 38% of fourth-graders cannot read an age-appropriate book. The following data show the number of children, by age, identified as learning disabled under special education. Most of these children have reading problems that should be identified and corrected before third grade. Current federal law prohibits most children from receiving extra help from special educational programs until they fall behind by approximately two years' worth of learning, and that typically means third grade or later (usa today sept. 6. 2001)

Age number of children

6 37,369

7 87,436

8 160,840

9 239, 719

10 286, 719

11 306, 533

12 310, 787

13 302, 604

14 289, 168

Suppose that we want to select a sample of children identified as learning disabled under special education for a program designed to improve reading ability. Let x be a random variable indicating the age of one randomly selected child.

A. Use the data to develop a probability distribution for x. Specify the values for the random variable and the corresponding values for the probability function f(x).

B Draw a graph of the probability distribution.

C. Show that the probability distribution satisfies equations (5.1) and (5.2)

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5. To perform a certain type of blood analysis, lab technicians must perform two procedures. The first procedure requires either one or two separate steps, and the second procedure requires either one, two, or three steps.

A. List the experimental outcomes associated with performing the blood analysis.

B. If the random variable of interest is the total number of steps required to do the complete analysis (both procedures), show what value the random variable will assume for each of the experimental outcomes?

Possible Outcomes Value of Variable

first procedure second ...