Given the kernel density estimator , show that it is a density for every N, and every and every relization of the sample ie. show the funciton is nonnegative and integrates to one.
I'm not sure how to formalise thise, I know that if is a density, then it integates to one by definition. Does the following work;
So I know that
needs to equal but I'm not sure what to do with the integral..