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Chapter 5: Discrete Probability Distributions

Chapter 5: Discrete Probability Distributions. Sections 5.1-5.2. Review of terms from Ch 1. Variable-. A characteristic or attribute that can assume different values. Random Variable-. A variable whose values are determined by chance. Review of terms from Ch 1.

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Chapter 5: Discrete Probability Distributions

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  1. Chapter 5: Discrete Probability Distributions Sections 5.1-5.2

  2. Review of terms from Ch 1 Variable- A characteristic or attribute that can assume different values Random Variable- A variable whose values are determined by chance

  3. Review of terms from Ch 1 Two Types of Random Variables: 1 - Discrete Variable- Has values that can be counted Examples: 1) outcomes for rolling a die 2) outcomes for tossing a coin 3) number of students making A’s

  4. Review of terms from Ch 1 Two Types of Random Variables: 2- Continuous Variable- Obtained from data that can be counted instead of measured Examples: 1) heights 2) weights 3) temperature 4) time

  5. Review of terms from Ch 1 Probability Distributions Consists of values a random variable can assume, X, And the corresponding probabilities of the values, P(X)

  6. Example 1: Construct a probability Distribution for rolling a single die.

  7. Example 1: Construct a probability Distribution for rolling a single die. Graphing: If you were to graph, what do you start with? 2/6 1/6 Probabilities P(X) 1 2 3 4 5 6 Outcomes (what you roll)

  8. Example 2: Construct a probability distribution and graph the results for the number of tails whentossing 3 coins. H T T H T H H T H T H T H T Sample Space: { HHH, THH, HTH, TTH, HHT, THT, HTT, TTT}

  9. Example 2: Construct a probability distribution and graph the results for the number of tails whentossing 3 coins. Sample Space: { HHH, THH, HTH, TTH, HHT, THT, HTT, TTT} 0 1 2 3 1/8 3/8 3/8 1/8

  10. Example 2: Construct a probability distribution and graph the results for the number of tails when tossing 3 coins. 3/8 2/8 Probabilities P(X) 1/8 0 1 2 3 Outcomes (# of tails)

  11. Example 3: The following is a frequency Distribution for the number of bedrooms In randomly selected homes listed for sale In a particular region of the country.

  12. Example 3: The following is a frequency Distribution for the number of bedrooms In randomly selected homes listed for sale In a particular region of the country. 1 2 3 4 5 .05 .15 .3 .42 .08

  13. Example 3: .5 .4 .3 .2 Probabilities P(X) .1 1 2 3 45 Outcomes (# bedrooms)

  14. Two requirements for a probability distribution: The _____ of the probabilities of all of the events in the sample space ___________. sum must equal 1 ΣP(X) = 1 The _________ of each event in the sample space must be ________________________. probability between or equal to 0 and 1 0 ≤ P(X) ≤ 1

  15. Determine whether or not each distribution is a probability distribution. 1) Yes!

  16. Determine whether or not each distribution is a probability distribution. 2) No, 1/8 + 1/8 + 3/8 + 1/8 = 6/8 which is not equal to 1.

  17. Determine whether or not each distribution is a probability distribution. 3) No, -0.1 is not between or equal to 0 and 1.

  18. Determine whether or not each distribution is a probability distribution. 2) Yes

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