Results 1 to 3 of 3

Math Help - Independence PMF

  1. #1
    Newbie
    Joined
    Mar 2010
    Posts
    2

    Independence PMF

    Hey guys,

    I need a little help with this prove. The question is to prove from both sides; so going left to right was easy but right to left, I couldn't figure it out! any suggestion how can I do this?

    Pr[X = x; Y = y] = Pr[X = x]Pr[Y = y] , for all x & y belong to R
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Danneedshelp's Avatar
    Joined
    Apr 2009
    Posts
    303
    Quote Originally Posted by Mohammed View Post
    Hey guys,

    I need a little help with this prove. The question is to prove from both sides; so going left to right was easy but right to left, I couldn't figure it out! any suggestion how can I do this?

    Pr[X = x; Y = y] = Pr[X = x]Pr[Y = y] , for all x & y belong to R
    Notice P(Y=y)=P(Y=y|X=x) or equivalently p(y)=p(y|x), since both X and Y are assumed to independent. So, using the latter notation we have that

    p(x)p(y)=p(x)p(y|x)=p(x,y).
    Follow Math Help Forum on Facebook and Google+

  3. #3
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    There's nothing to prove here.
    this is a valid definition of independence between two random variables.

    you can prove that ....

    P(X|Y)=P(X) is equivalent to P(X,Y)=P(X)P(Y)

    but you have half of a statement.



    Quote Originally Posted by Mohammed View Post
    Hey guys,

    I need a little help with this prove. The question is to prove from both sides; so going left to right was easy but right to left, I couldn't figure it out! any suggestion how can I do this?

    Pr[X = x; Y = y] = Pr[X = x]Pr[Y = y] , for all x & y belong to R
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: November 15th 2010, 02:24 PM
  2. Independence
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: February 6th 2010, 08:41 PM
  3. independence
    Posted in the Advanced Statistics Forum
    Replies: 8
    Last Post: January 27th 2010, 11:29 PM
  4. Independence with mod
    Posted in the Number Theory Forum
    Replies: 5
    Last Post: September 18th 2009, 11:53 PM
  5. independence
    Posted in the Advanced Statistics Forum
    Replies: 7
    Last Post: September 5th 2009, 11:53 PM

Search Tags


/mathhelpforum @mathhelpforum