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Chapter 5 Probability Distributions

Chapter 5 Probability Distributions. In this handout: Expectation (mean) Standard deviation Bernoulli trials Binomial distribution. Expectation (mean) of a probability distribution. Ex.: Computing the mean for the example of tossing three coins.

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Chapter 5 Probability Distributions

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  1. Chapter 5Probability Distributions In this handout: Expectation (mean) Standard deviation Bernoulli trials Binomial distribution

  2. Expectation (mean) of a probability distribution Ex.: Computing the mean for the example of tossing three coins.

  3. Box on Page 187Variance and Standard Deviation of X

  4. Table 5.7 (p. 188)Calculation of Variance and Standard Deviation

  5. Examples of Bernoulli trials: - tossing a coin: tail or head- testing a product: good or defective item

  6. Boxes on Page 197Probability model; the Binomial Distribution

  7. Elementary outcomes with associated probabilities in case of four trials

  8. Figure 5.3 (p. 200)Binomial distributions for n = 6.

  9. How to use the binomial table (Appendix B, Table 2) For example, P[X=2] = f(2) = (table entry at c=2) – (table entry at c=1)

  10. E.g., for the binomial distribution with n=3 and p=.5,Mean = np = 3×.5 = 1.5Variance = npq = 3×.5 ×.5 = .75

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