1 / 14

Probability Distributions

Probability Distributions. Gordon Stringer University of Colorado, Colorado Springs. Probability Distributions. Probability Mass Function Assign each specific probability of that outcome Cumulative Distribution Function

kemp
Download Presentation

Probability Distributions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript


  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

More Related