x ~ N(a,b), x ~ N(c,d). x and y are independent Random Variables.

I am trying to compute this expectation:-

E[f(x,y)]..... x Where f(x,y) = y if (x-y)>0 f(x,y) = x, if otherwise

The way I was thinking is

E[f(x,y)] = yP((x-y)>0) + x(1-P((x-y)>0))

P((x-y)>0 is something I can compute from the distributions of x and y, but E[f(x,y)] is not giving a closed form solution it's still having randomness as I still don't know what x and y can be.

Any help is appreciated.

x ~ N(a,b), y ~ N(c,d). x and y are independent Random Variables.

I am trying to compute this expectation:-

E[f(x,y)]..... x Where f(x,y) = y if (x-y)>0 f(x,y) = x, if otherwise

The way I was thinking is

E[f(x,y)] = yP((x-y)>0) + x(1-P((x-y)>0))

P((x-y)>0 is something I can compute from the distributions of x and y, but E[f(x,y)] is not giving a closed form solution it's still having randomness as I still don't know what x and y can be.

Any help is appreciated.