3 Other Distributions

3 Other Distributions - Dr. Harvey A. Singer School of...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
© 2002 by Harvey A. Singer 1 OM 210:  Statistical Analysis for  Management 3. Other Continuous Distributions Dr. Harvey A. Singer School of Management George Mason University
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
© 2002 by Harvey A. Singer 2 Learning Objectives 1. Describe the exponential and uniform probability distributions. 2. Solve probability problems involving these distributions.
Background image of page 2
© 2002 by Harvey A. Singer 3 Continuous Probability Distribution Models Continuous Probability Distributions Normal Exponential Uniform
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
© 2002 by Harvey A. Singer 4 Exponential Distribution A continuous probability distribution that, for a Poisson process, describes the chances of observing specific lengths of intervals between occurrences of an event. The intervals may be in time, length, distance, space. E.g., the time that elapses between occurrences. The chance of having to wait a specific amount of time between occurrences. Occurrences may be arrivals.
Background image of page 4
© 2002 by Harvey A. Singer 5 Exponential Distribution The probability that the interval x between occurrences will be as much as (but no bigger than) x is: λ =expected (mean) number of occurrences per unit interval. λ is the Poisson mean. x = any particular specified length of interval between occurrences. ( 29 x e x X Prob λ - - = λ 1 |
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
© 2002 by Harvey A. Singer 6 Rate vs. Interval If events are expected to occur at the rate λ , then 1/ λ is the expected (mean) interval between events. If λ is the mean rate, then 1/ λ is the mean interval between occurrences. E.g., if events occur at the mean rate of λ per unit time, then 1/ λ is the average time to wait between occurrences.
Background image of page 6
© 2002 by Harvey A. Singer 7 Exponential Distribution Graphs 0.0 0.2 0.4 0.6 0.8 1.0 0 5 10 15 20 25 30 x Prob (x) 0.05 0.10 0.50 1 2
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
© 2002 by Harvey A. Singer 8 Waiting Limits If the chance of waiting as long as x between occurrences is then the chance of waiting longer than x between occurrences is the compliment, viz ( 29 ( 29 x x e x X Prob e x X Prob λ - λ - = λ - = λ | 1 |
Background image of page 8
© 2002 by Harvey A. Singer
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 28

3 Other Distributions - Dr. Harvey A. Singer School of...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online