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# PADM 7060 Quantitative Methods for Public Administration Unit 3 Chapters 9-10 - PowerPoint PPT Presentation

PADM 7060 Quantitative Methods for Public Administration Unit 3 Chapters 9-10. Fall 2004 Jerry Merwin. Meier &amp; Brudney Part III: Probability. Chapter 7: Introduction to Probability Chapter 8: The Normal Probability Distribution Chapter 9: The Binomial Probability Distribution

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Fall 2004

Jerry Merwin

Meier & BrudneyPart III: Probability
• Chapter 7: Introduction to Probability
• Chapter 8: The Normal Probability Distribution
• Chapter 9: The Binomial Probability Distribution
• Chapter 10: Some Special Probability Distributions
• What is the binomial probability distribution?
• What is a Bernoulli process?
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 2)
• Let’s discuss the characteristics of a Bernoulli process: (book says two, but can be three)
• Each trial’s outcome must be mutually exclusive: Success or failure
• Probability of success (p) remains constant (as does probability of failure, q)
• Trials are independent (Not affected by outcomes of earlier trials)
• Examples:
• Coin flip
• Roll of die (six or not six)
• Fire in a community
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 3)
• More on Bernoulli process - Must how three things to determine probability:
• Number of trials
• Number of successes
• Probability of success in any trial
• Formula (see page 146)
• Combination of n things taken r at a time
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 4)
• Let’s look at some examples:
• Starting at the bottom of page 146:
• How many sets of three balls can be selected from four balls (a, b, c, d)?
• How many combinations of four things two at a time?
• We can list the possibilities with these examples to come up with solutions.
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 5)
• What if we do not want to list all the combinations?
• See the formula on page 147
• Do you understand how to calculate a factorial?
• Examples of formula with coin flip (pages 147-149)
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 6)
• What is the problem with calculating factorials?
• Cumbersome in larger numbers!
• So what alternative do we have?
• How can the normal curve be used?
• A general rule‑of‑thumb is that once n ≥ 30, the normal distribution can be used to calculate the binomial probability distribution.
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 7)
• How about the problem on the Republican’s chance of being hired in Chicago? (Page 151)
• See the information for the binomial distribution
• The standard deviation of a probability distribution at the bottom of 151
• Simply convert the number actually hired into a z score and look up the value.
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 8)
• On page 152, you\'re told that you should use this only when n x p is greater than 10 and n x (1 -p) is greater than 10.
• Also, keep in mind that the normal curve tells you the probability only that r or fewer (or more) events occurred. It does not tell you the probability of exactly r events occurring.
• This probability can be determined only by using the binomial distribution.
Meier & Brudney: Chapter 9 The Binomial Probability Distribution (Page 9)
• Problems: 9.2 & 9.6
Meier & Brudney: Chapter 10 Special Probability Distributions
• What is the Hypergeometric Probability Distribution and when is it used?
• When you have a finite population the hypergeometric probability distribution is better than the binomial distribution.
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 2)
• Let’s look at the Andersonville City Fire department example (pp. 157-158).
• There are 34 women out of a pool of 100 eligible applicants.
• The p = .34, and 30 trials (n = 30).
• Thus your mean is:  = 30 x .34 = 10.2.
• The key difference is in computing the standard deviation.
• The formula is shown on page 158 and the answer is on 159.
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 3)
• What is The Poisson distribution?
• It is named for the Frenchman, Simeon Dennis Poisson, who developed it in the first half of the 19th century.
• It is used to describe a pattern of behavior when some event occurs at varying, random intervals over a continuum of time, length, or space.
• Your text uses muggings & potholes as examples.
• It has been widely used to describe the probability functions of phenomena such as product demand; demand for services; # of calls through a switchboard; passenger cars at toll stations, etc.
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 4)
• How is the Poisson distribution different from the Bernoulli process?
• The number of trials is not known in a Poisson process.
• Instead, the Poisson distribution is concerned with a discrete, random variable which can take on the values x = 0,1,2,3 . . . where the three dots mean "ad infinitum".
• The formula is:  = xe-/x! (see page 160)
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 5)
• The formula is:  = xe-/x!
• where:
•  (lambda) = the probability of an event
• x = # of occurrences
• e = 2.71828 (a constant that is the base of the Naperian or natural logarithm system)
• Fortunately, this is not something we need to calculate;
• we\'ll use Table 2 (pp. 444-445), as we are sane.
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 6)
• Let’s look at the management example on pages 160-161.
• Why does the Poisson table only go to 20 for the λvalues?
• We can use the normal distribution table for those values above 20.
Meier & Brudney: Chapter 10 Special Probability Distributions (Page 7)
• Problems 10.2, 10.4, 10.6, & 10.16