given that f(x,y)= exp(-x^2+y^2/2), find probability of X+Y<1 when (X,Y) has this density.
my book said that dividing f(x,y) by a constant K will produce a bivariate pdf. hence the P(X+Y<1) would be a double integral over f(x,y) /K.
why do we need to divide by K and how do we know when to divide by K?
Next I do not think that you should just integrate x and y; e.g., over y from -oo to 1-x, and then over x from -oo to +oo. The reason is that you will get an error function for the integral over y, which makes it unnecessary difficult to do the integral over x. Instead it seems better to change to new variables; w=x+y and z=x-y looks good.