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Probability Distributions

Probability Distributions

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Probability Distributions

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  1. Probability Distributions • Gordon Stringer • University of Colorado, Colorado Springs

  2. Probability Distributions • Probability Mass Function • Assign each specific probability of that outcome • Cumulative Distribution Function • Assign a probability of less than or equal to the probability of the outcome

  3. Probability Distributions • Continuous Probability • Predicting rainfall • Infinite possible out comes

  4. Probability Distributions • Fractiles • 01 = 1/100 chance • .25 • .50 • .75 • .99 • Between 0 and 1.000

  5. Probability Distributions • Personal judgment • Considered to the “Subjective Method” • Flying on a Friday/Sunday • “ My best guess is my plane will be late”

  6. Probability Distributions • Historical Data • More concrete • Provides evidence • Separates data from guess work • Data up to “interpretation” or judgment is involved • Indistinguishable situations

  7. Probability Distributions • Historical Data • Lots of data points help build a clear picture • Few data points leave room for error. • Collecting data is usually expensive

  8. Probability Distributions • Binomial Distribution • Poisson Distribution • Normal Distribution • Exponential Distribution

  9. Probability Distributions • Binomial Distribution • p and (1-p) • Identical and independent trials • Success/ Failure • Heads / Tails • =BINOMDIST(x,n,p,cumulative)

  10. Probability Distributions • Normal Distribution • Independent trials • Bell-shaped curve • Central Limit Theorem: As the number of trials get large, the distribution becomes increasingly normal • Central Tendency = Mean • Dispersion = Standard Deviation

  11. Probability Distributions • Normal Distribution • Differing means vs. differing Std Dev • 1s = .6826 • 2s = .9544 • 3s = .9974 • =NORMDIST(x,u,s,Cumulative) • Grear Tire example (see ProbDist.xls)

  12. Probability Distributions • Poisson Distribution • Number of events in time • Independent • =POISSON(x,u,cumulative) • Mercy Hospital example:

  13. Probability Distributions Mean = 6 Arrivals /Hour • P(3) in 20 minutes • P(1) in 10 minutes • P(>1) in 20 minutes • P(<6) in 30 minutes

  14. Probability Distributions • Exponential Distribution • Distribution of time until the next event in a time series of events • =EXPONDIST(x,u,cumulative) • Schips Loading Dock example • See ProbDist.xls