Review the following concepts if necessary:

- Discrete Random Variables for Beginning Statistics
- Binomial Random Variable for Beginning Statistics
- Tables of The Binomial Distribution for Beginning Statistics
- Poisson Random Variable and Probability Formula for Beginning Statistics
- Hypergeometric Random Variable and Probability Formula for Beginning Statistics

### Random Variable

- A taste test is conducted involving 35 individuals. Random variable X is the number in the 35 who prefer a locally produced nonalcoholic beer to a national brand. What are the possible values for X?
- A psychological experiment was conducted in which the time to traverse a maze was recorded for each of five dogs. The times were 4, 6, 8, 9, and 12 minutes. Two of the times were randomly selected and the difference X = largest of the pair – smallest of the pair was recorded. Give all possible pairs of possible selections, and the value of X for each outcome.

*Ans*. The whole numbers 0 through 35

*Ans*. See Table 5.18.

### Discrete Random Variable

- A die is tossed until the face 6 turns up. Let X be the number of tosses needed until the face 6 first turns up. Give the possible values for the variable X.
- Identify the discrete random variables in parts (
*a*) through (*e*).- The number of arrests during a 10-day period during which the police apply a Zero-tolerance strategy
- The time workers have spent with their current employer
- The number of nurse practitioners per state
- The career lifetime of major league baseball players
- The number of executions of death row inmates per year in the U.S.

*Ans*. The possible values are the positive integers. That is, the possible values are 1, 2, 3, . . . .

*Ans*. (*a*), (*c*), and (*e*)

### Continuous Random Variable

- Identify the continuous random variables in the following list.
- Weight of individuals in kg
- Serum cholesterol level in mg/dl
- Length of intravenous therapy in hours
- Body mass index in kg/m
^{2} - Cardiac output in liters/minute

- What is the primary difference between a discrete random variable and a continuous random variable?

*Ans*. All five are continuous.

*Ans*. There are values between the possible values of a discrete random variable which are not possible values for the random variable. This is not generally true for a continuous random variable.

### Probability Distribution

- Suppose Table 5.19 gives the number in thousands of students in grades 9 through 12 for public schools in the United States. Let X represent the grade level. Give the probability distribution for X.
- Which of the following are probability distributions? For those which are not, tell why they are not.
- P(x) = .2x
^{2}, x = 1, 2

- P(x) = .2x

*Ans*. The distribution is given in Table 5.20.

*Ans*. Parts (*b*) and (*d*) are probability distributions. Part (*a*) is not because Σ P(x) = 1.2. Part (c) is not because P(50) < 0.

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