1 / 11

Continuous Probability Distributions

. b. a. . . Continuous Probability Distributions. The Uniform Distribution. The Normal Distribution. The Exponential Distribution. . . b. b. a. a. x 1. x 2. x 1. The Uniform Probability Distributions. . b. a. x 1. P(x 1 ≤ x ≤ x 2 ). P(x ≤ x 1 ).

Télécharger la présentation

Continuous 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. b a   Continuous Probability Distributions • The Uniform Distribution • The Normal Distribution • The Exponential Distribution

  2.  b b a a x1 x2 x1 The Uniform Probability Distributions  b a x1 P(x1≤x≤ x2) P(x≤ x1) P(x≥ x1)= 1- P(x<x1) P(x≥ x1)

  3. The Uniform Probability Distribution • Uniform Probability Density Function f (x) = 1/(b - a) for a<x<b = 0 elsewhere where a = smallest value the variable can assume b = largest value the variable can assume The probability of the continuous random variable assuming a specific value is 0. P(x=x1) = 0

  4. The Normal Probability Density Function where  = mean  = standard deviation  = 3.14159 e = 2.71828

  5. The Normal Probability Distribution • Graph of the Normal Probability Density Function f (x ) x 

  6. The Standard Normal Probability Density Function where  = 0  = 1  = 3.14159 e = 2.71828

  7. The table will give this probability Given positive z Given any positive value for z, the table will give us the following probability The probability that we find using the table is the probability of having a standard normal variable between 0 and the given positive z.

  8. Given z = .83 find the probability

  9. The Exponential Probability Distribution • Exponential Probability Density Function for x> 0,  > 0 where  = mean e = 2.71828 • Cumulative Exponential Distribution Function wherex0 = some specific value of x

  10. Example The time between arrivals of cars at Al’s Carwash follows an exponential probability distribution with a mean time between arrivals of 3 minutes. Al would like to know the probability that the time between two successive arrivals will be 2 minutes or less. P(x< 2) = 1 - 2.71828-2/3 = 1 - .5134 = .4866

  11. F (x ) .4 P(x< 2) = area = .4866 .3 .2 .1 x 1 2 3 4 5 6 7 8 9 10 Example: Al’s Carwash • Graph of the Probability Density Function

More Related