SECTION 4.1 Probability Distributions 191 Discrete Variables and Continuous Variables Determine whether each random variable x is discrete or continuous. Explain your reasoning. 1. Let x represent the number of Fortune 500 companies that lost money in the previous year. 2. Let x represent the volume of gasoline in a 21-gallon tank. SOLUTION 1. The number of Fortune 500 companies that lost money in the previous year can be counted. The set of possible outcomes is 50, 1, 2, 3, . . ., 5006. So, x is a discrete random variable. 2. The amount of gasoline in the tank can be any volume between 0 gallons and 21 gallons. So, x is a continuous random variable. TRY IT YOURSELF 1 Determine whether each random variable x is discrete or continuous. Explain your reasoning. 1. Let x represent the speed of a rocket. 2. Let x represent the number of calves born on a farm in one year. 3. Let x represent the number of days of rain for the next three days. Answer: Page A38 It is important that you can distinguish between discrete and continuous random variables because different statistical techniques are used to analyze each. The remainder of this chapter focuses on discrete random variables and their probability distributions. Your study of continuous probability distributions will begin in Chapter 5. Discrete Probability Distributions Each value of a discrete random variable can be assigned a probability. By listing each value of the random variable with its corresponding probability, you are forming a discrete probability distribution. A discrete probability distribution lists each possible value the random variable can assume, together with its probability. A discrete probability distribution must satisfy these conditions. In Words In Symbols 1. The probability of each value of the discrete 0 … P1x2 … 1 random variable is between 0 and 1, inclusive. 2. The sum of all the probabilities is 1. ΣP1x2 = 1 DEFINITION Because probabilities represent relative frequencies, a discrete probability distribution can be graphed with a relative frequency histogram. EXAMPLE 1 Study Tip Values of variables such as volume, age, height, and weight are sometimes rounded to the nearest whole number. These values represent measured data, however, so they are continuous random variables.
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