f[x_,y_] := Exp[(-1/(2(1-r^2))) (( ((x-m1)/s1)^2 - 2 r (x-m1)/s1 (y-m2)/s2) + ((y-m2)/s2)^2)] / (2 Pi s1 s2 Sqrt[1-r^2])

Plot3D[f[x,y],{x,-4,4},{y,-4,4}]

f[x,y]

f[x,y]/. m1->0

%/. m2->0

%/. s1->1

% /. s2->1

%/. r->0

Plot3D[Out[40], {x,-3,3},{y,-3,3}]

Integrate[Out[40],{x,-Infinity,Infinity}]

Integrate[%,{y,-Infinity,Infinity}]

Manipulate[{r,Plot3D[Out[39],{x,-3,3},{y,-3,3}]},{r,-.9,.9}]