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Understanding Random Variables: Exploring Probability Distributions

This chapter combines methods from Chapters 1 and 6 to construct probability distributions. Probability distributions predict likely outcomes. Learn to form a theoretical behavior model using descriptive statistics and probabilities.

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Understanding Random Variables: Exploring Probability Distributions

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  1. Chapter 7 Random Variables

  2. Overview This chapter will deal with the construction of probability distributions by combining the methods of Chapter 1 with the those of Chapter 6. Probability Distributions will describe what will probably happen instead of what actually did happen.

  3. Combining Descriptive Statistics Methods and Probabilities to Form a Theoretical Model of Behavior Chapter 7 Chapter 1 Chapter 6

  4. § 7.1 Random Variables

  5. Definitions • Random Variable a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure • Probability Distribution a graph, table, or formula that gives the probability for each value of the random variable

  6. Table 4-1 Probability DistributionNumber of Girls Among Fourteen Newborn Babies x P(x) 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 0.000 0.001 0.006 0.022 0.061 0.122 0.183 0.209 0.183 0.122 0.061 0.022 0.006 0.001 0.000

  7. Definitions • Discrete random variable has either a finite number of values or countable number of values, where ‘countable’ refers to the fact that there might be infinitely many values, but they result from a counting process.

  8. Probability Histogram Figure 4-3

  9. Example: JSL Appliances • Discrete random variable with a finite number of values Let x = number of TV sets sold at the store in one day where x can take on 5 values (0, 1, 2, 3, 4) • Discrete random variable with an infinite sequence of values Let x = number of customers arriving in one day where x can take on the values 0, 1, 2, . . . We can count the customers arriving, but there is no finite upper limit on the number that might arrive.

  10. Definitions • Continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale with no gaps or interruptions.

  11. Requirements for Probability Distribution

  12. Requirements for Probability Distribution  P(x) = 1 where x assumes all possible values

  13. Requirements for Probability Distribution  P(x) = 1 where x assumes all possible values 0 P(x) 1 for every value of x

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