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Discrete Random Variables Supplementary Problems for Beginning Statistics

By — McGraw-Hill Professional
Updated on Aug 12, 2011

Review the following concepts if necessary:

Random Variable

  1. 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?
  2. Ans.   The whole numbers 0 through 35

  3. 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.
  4. Ans.   See Table 5.18.

Discrete Random Variable

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

  3. Identify the discrete random variables in parts (a) through (e).
    1. The number of arrests during a 10-day period during which the police apply a Zero-tolerance strategy
    2. The time workers have spent with their current employer
    3. The number of nurse practitioners per state
    4. The career lifetime of major league baseball players
    5. The number of executions of death row inmates per year in the U.S.
  4. Ans.   (a), (c), and (e)

Continuous Random Variable

  1. Identify the continuous random variables in the following list.
    1. Weight of individuals in kg
    2. Serum cholesterol level in mg/dl
    3. Length of intravenous therapy in hours
    4. Body mass index in kg/m2
    5. Cardiac output in liters/minute
  2. Ans.   All five are continuous.

  3. What is the primary difference between a discrete random variable and a continuous random variable?
  4. 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

  1. 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.
  2. Ans.   The distribution is given in Table 5.20.

  3. Which of the following are probability distributions? For those which are not, tell why they are not.
    1. P(x) = .2x2 , x = 1, 2
  4. 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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