1. © 2001 Prentice-Hall, Inc.Chap 5-1 BA 201 Lecture 8 Some Important Discrete Probability Distributions

2. © 2001 Prentice-Hall, Inc. Chap 5-2 Topics Binomial Distribution Poisson Distribution

3. © 2001 Prentice-Hall, Inc. Chap 5-3 Important Discrete Probability Distributions Discrete Probability Distributions BinomialPoisson

4. © 2001 Prentice-Hall, Inc. Chap 5-4 Binomial Probability Distribution ‘n’ Identical Trials E.g. 15 tosses of a coin; 10 light bulbs taken from a warehouse 2 Mutually Exclusive Outcomes on Each Trials E.g. Head or tail in each toss of a coin; defective or not defective light bulb Trials are Independent The outcome of one trial does not affect the outcome of the other

5. © 2001 Prentice-Hall, Inc. Chap 5-5 Binomial Probability Distribution Constant Probability for Each Trial E.g. Probability of getting a tail is the same each time we toss the coin 2 Sampling Methods Infinite population without replacement Finite population with replacement (continued)

6. © 2001 Prentice-Hall, Inc. Chap 5-6 Binomial Probability Distribution Function E.g. Tails in 2 Tosses of Coin X P(X) 0 1/4 =.25 1 2/4 =.50 2 1/4 =.25

7. © 2001 Prentice-Hall, Inc. Chap 5-7 Binomial Distribution Characteristics Mean E.g. Variance and Standard Deviation E.g. n = 5 p = 0.1 0.2.4.6 012345 X P(X)

8. © 2001 Prentice-Hall, Inc. Chap 5-8 Binomial Distribution in PHStat PHStat | Probability & Prob. Distributions | Binomial Example in Excel Spreadsheet when n=5, p=.1

9. © 2001 Prentice-Hall, Inc. Chap 5-9 Poisson Distribution Poisson Process: Discrete events in an “interval” The probability of One Success in an interval is stable The probability of More than One Success in this interval is 0 The probability of success is independent from interval to interval E.g. # customers arriving in 15 min. E.g. # defects per case of light bulbs PXx x x (| !  e -

10. © 2001 Prentice-Hall, Inc. Chap 5-10 Poisson Probability Distribution Function E.g. Find the probability of 4 customers arriving in 3 minutes when the mean is 3.6.

11. © 2001 Prentice-Hall, Inc. Chap 5-11 Poisson Distribution in PHStat PHStat | Probability & Prob. Distributions | Poisson Example in Excel Spreadsheet

12. © 2001 Prentice-Hall, Inc. Chap 5-12 Poisson Distribution Characteristics Mean Standard Deviation and Variance  = 0.5  = 6 0.2.4.6 012345 X P(X) 0.2.4.6 0246810 X P(X)

13. © 2001 Prentice-Hall, Inc. Chap 5-13 Summary Discussed Binomial Distribution Addressed Poisson Distribution