4.1 EXERCISES SECTION 4.1 Probability Distributions 197 For Extra Help: MyLab® Statistics Building Basic Skills and Vocabulary 1. What is a random variable? Give an example of a discrete random variable and a continuous random variable. Justify your answer. 2. What is a discrete probability distribution? What are the two conditions that a discrete probability distribution must satisfy? 3. Is the expected value of the probability distribution of a random variable always one of the possible values of x? Explain. 4. What does the mean of a probability distribution represent? True or False? In Exercises 5–8, determine whether the statement is true or false. If it is false, rewrite it as a true statement. 5. In most applications, continuous random variables represent counted data, while discrete random variables represent measured data. 6. For a random variable x, the word random indicates that the value of x is determined by chance. 7. The mean of the random variable of a probability distribution describes how the outcomes vary. 8. The expected value of a random variable can never be negative. Graphical Analysis In Exercises 9–12, determine whether the graph on the number line represents a discrete random variable or a continuous random variable. Explain your reasoning. 9. The attendance at concerts for 10. The length of time student musicians a rock group practice each week 40,000 45,000 50,000 Attendance 0 4 8 12 16 20 Time (in hours) 11. The distance a baseball travels 12. The total annual arrests (in millions) after being hit in the United States (Source: U.S. 0 200 400 600 100 300 500 Distance (in feet) Department of Justice) 11 10 12 13 Arrests Using and Interpreting Concepts Discrete Variables and Continuous Variables In Exercises 13–18, determine whether the random variable x is discrete or continuous. Explain. 13. Let x represent the number of cars in a university parking lot. 14. Let x represent the length of time it takes to complete an exam. 15. Let x represent the volume of blood drawn for a blood test. 16. Let x represent the populations of the 50 U.S. states. 17. Let x represent the fitted hat sizes of members of a softball team. 18. Let x represent the snowfall (in inches) in Nome, Alaska, last winter.
RkJQdWJsaXNoZXIy NjM5ODQ=