1 / 8

ch3

Multionariate. ch3. Random Variables. Multionariate Random Variables. 3.1. Cumulative. distribution function. Cumulative distribution function. Definition 3.1. Let S be the sample space associated with a particular. experiment. X and Y be two r.v. assigning to.

sanaa
Download Presentation

ch3

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. Multionariate ch3 Random Variables Multionariate Random Variables

  2. 3.1 Cumulative distribution function Cumulative distribution function

  3. Definition 3.1 Let S be the sample space associated with a particular experiment. X and Y be two r.v. assigning to a real number vector, (X, Y) , are called Denoted by (X,Y) two-dimensionalrandom variable.

  4. a) Joint cdf Definition 3.2 Let X, Y be two random variables. The joint cumulative distribution function (cdf) of bivariate r. v. (X, Y)is defined as

  5. Properties of bivariate cdf F(x,y) (1) F(x,y) is non-decreasing about x and y. i.e. (2)

  6. (3) F(x,y) is right continuous in each argument, i.e. (4) 0

  7. b) marginal cdf Definition 3.3 If FX,Y (x,y) is the joint cdf of the r.v.s X and Y, then the cdfs FX(x) and FY(y) of X and Y are called marginal cdfs of X and Y, respectively. Obviously the marginal cdf can be determined by the joint cdf. i.e.

More Related