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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.

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ch3

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  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.

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