3 Other Distributions

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

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© 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

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© 2002 by Harvey A. Singer 2 Learning Objectives 1. Describe the exponential and uniform probability distributions. 2. Solve probability problems involving these distributions.
© 2002 by Harvey A. Singer 3 Continuous Probability Distribution Models Continuous Probability Distributions Normal Exponential Uniform

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© 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.
© 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 |

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© 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.
© 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

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© 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 |
© 2002 by Harvey A. Singer

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

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