Re: PDF- Sinistral, have a look.

Posted by Sinistral on Jun 18, 2013; 4:51pm
URL: http://discussion-forum.276.s1.nabble.com/PDF-Sinistral-have-a-look-tp7582516p7582551.html

Oh yes!! how could I miss that. (thank you so much Sir)

EDIT
F(u,v)= Pr(U<u, V<v)= Pr(U<u, V<v|X<Y) Pr(X<Y) + P(U<u, V<v|X>Y) Pr(X>Y)   (as pointed by Amit Sir and now it seems fairly obvious).
                              Pr(U<u, V<v AND X<Y) * Pr(X<Y)     +    P(U<u, V<v AND X>Y) * Pr(X>Y)
                         =   --------------------------------          ----------------------------
                                        Pr(X<Y)                                                   Pr(X>Y)


                         =               P ( X<u,Y<v)                     +                P (Y<u,X<v)
/EDIT

Rest of the solution is same:

        =P( X<u)*P(Y<v) + P(Y<u)*P(X<v)  since X and Y are independent.
         = Integral (x=0 to u) 2x^2 dx * Integral(y=0 to v) 3y^3 dy   + Integral(y=0 to u) 3y^3 dy * Integral (x=0 to v) 2x^2 dx
         =u^2*v^3  + v^2*u^3
         
f(u,v)=  ∂²F(u,v)/∂u∂v
        = 6uv(u+v)      0<u<v<1