2/14/2011

General summary of probability distributions

• Binomial distribution - number of successes in n independent Bernoulli trials
• Poisson distribution - another probability model for the number of events (successes)
• Geometric distribution - waiting for the first success with independent Bernoulli trials.
• Negative binomial distribution - waiting for the rth success with independent Bernoulli trials
• Multinomial distribution - a discrete distribution for the number of events in more than two different categories

Probability Distributions with Minitab

Graph > Probability Distribution Plot

Binomial Distributions - Calc > Probability Distributions Binomial

• Probability - P(X=x)
• Cumulative Probability - P(X<=x)
• Inverse Cumulative Probability - Find percentiles

Geometric Distributions - Calc > Probability Distributions Geometric

• Same options (Probability, Cumulative Probability, or Inverse Cumulative Probability)

Poisson Distributions - Calc > Probability Distributions Poisson

• Same options (Probability, Cumulative Probability, or Inverse Cumulative Probability)

Negative Binomial Distributions - Calc > Probability Distributions Negative Binomial

• Same options (Probability, Cumulative Probability, or Inverse Cumulative Probability)

Chapter 6

Class discussion - questions on case studies 6-2 and 6-3.

Case Study 6-2 Modeling Runs Scored: Getting on Base

• Negative Binomial Distribution
• Expected Counts
• Pearson Residuals

Case Study 6-3 Modeling Runs Scored: Advancing the runners to home

• Multinomial probability distribution
• Independence
• Expected Counts
• Pearson Residuals

Class Exercises

Leadoff Exercise, 6.1, 6.3

Go to MLB.com and find the BA for your favorite player during the 2008 season.

• Graph the distribution for the number of at-bats until the first hit for this player.
• What is the probability that this player gets his first hit on the third at bat? fourth at bat? tenth at bat?
• What is the expected number of at-bats until your favorite player gets his first hit?
• Graph the distribution for the number of at-bats until the third hit.
• What is the probability that this player gets his third hit on his third at bat? fourth at bat? tenth at bat?

We will finish our discussion of probability distributions on Friday.