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

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

Box on Page 187 Variance and Standard Deviation of X

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

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

Boxes on Page 197 Probability model; the Binomial Distribution

Elementary outcomes with associated probabilities in case of four trials

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

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)

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