Re: [MATH] Probability question

[Sonnet Nguyen <Sonnet.Nguyen@fuw.edu.pl>]

Hi Thanh,

1. Use definition:
 
    f (x|y) = f   (x,y)/ f (y)
     X|Y       X,Y        Y
  
  here  f_{Y}(y):=f_{X,Y}(0,y)

2. Use general definition:
    P_{U)(A)=P_{V}({x^{n}: phi(x^{n}) \in A}) = P_{V}( phi^{-1}(A) ),
          
  here P is probab.,
       probab. vector variables  U,V: \Omega \to R^{n} and 
       U(\omega) = phi(V(omega)); (phi is a function from R^{n} to R^{k}.)

  and pdf = diff. of Probability;

  In your case, n=2 and phi(x,y)=x^{2}+y^{2}; 

Hope it's helpful,

SN
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|                     Sonnet Nguyen                     |
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