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Probability Distributions

Probability Distributions. Section 7.6. Definitions. Random Variable: values are numbers determined by the outcome of an experiment. (rolling 2 dice: rv’s  2 through 12) Probability Distribution: function which maps each value of a rv onto its probability.

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Probability Distributions

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  1. Probability Distributions Section 7.6

  2. Definitions • Random Variable: values are numbers determined by the outcome of an experiment. (rolling 2 dice: rv’s  2 through 12) • Probability Distribution: function which maps each value of a rv onto its probability. • Relative Frequency: Looks like a probability distribution, but in an experiment

  3. Expected Value • Weighted average! • Let be a probability distribution. The mean (or expected value) μ (mu) of the distribution is

  4. Example 1 Just for these notes, an author rolled two normal dice 9 times with the following sums: 6, 10, 11, 10, 9, 9, 12, 7, 9. • Mean? • Give the percent error between the mean and the expected value. 83/ 9 = 9.222 =31.7% =7

  5. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. • What is the domain of the RV? • Find the probability for each value of the rv • Construct a histogram of the probability distribution. • Find the expected value of the distribution.

  6. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. • What is the domain of the RV? {0, 1, 2, 3, 4}

  7. Example 2 There is a family with 4 children. Let the random variable of the distribution stand for the number of boys. b. Find the probability for each value of the rv

  8. Example 2 c. Construct a histogram of the probability distribution.

  9. Example 2 d. Find the expected value of the distribution. 0(1/16) + 1(4/16) + 2(6/16) + 3(4/16) + 4(1/16) = 2

  10. Homework Pages 461 – 462 3 – 6, 8 – 9 13 – 14

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