Probability Distributions 4.1 190 CHAPTER 4 Discrete Probability Distributions Random Variables Discrete Probability Distributions Mean, Variance, and Standard Deviation Expected Value What You Should Learn How to distinguish between discrete random variables and continuous random variables How to construct and graph a discrete probability distribution and how to determine whether a distribution is a probability distribution How to find the mean, variance, and standard deviation of a discrete probability distribution How to find the expected value of a discrete probability distribution Random Variables The outcome of a probability experiment is often a count or a measure. When this occurs, the outcome is called a random variable. A random variable x represents a value associated with each outcome of a probability experiment. DEFINITION The word random indicates that x is determined by chance. There are two types of random variables: discrete and continuous. A random variable is discrete when it has a finite or countable number of possible outcomes that can be listed. A random variable is continuous when it has an uncountable number of possible outcomes, represented by an interval on a number line. DEFINITION In most applications, discrete random variables represent counted data, while continuous random variables represent measured data. For instance, consider the following example. You conduct a study of the number of calls a business makes in one day. The possible values of the random variable x are 0, 1, 2, 3, 4, and so on. Because the set of possible outcomes 50, 1, 2, 3, . . .6 can be listed, x is a discrete random variable. You can represent its values as points on a number line. 012345678910 Number of Calls (Discrete) x can be any whole number: 0, 1, 2, 3, . . . A different way to conduct the study would be to measure the time (in hours) the business spends making calls in one day. Because the time spent making calls can be any number from 0 to 24 (including fractions and decimals), x is a continuous random variable. You can represent its values with an interval on a number line. 0 3 6 9 12 15 18 21 24 Hours Spent on Calls (Continuous) x can be any value between 0 and 24. When a random variable is discrete, you can list the possible values the variable can assume. However, it is impossible to list all values for a continuous random variable.
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