Question 1 No code is required for this question. Consider an i.i.d. sample {X 1, . . . , X N} and a non-parametric estimate f of its probability density function f dened for any a E R and some real constant it > 0 by fa) = $in (X?) (a) What is the standard deviation of function K(a)? (No derivations are required to answer this question.) (b) What is the stande deviation of function Kh(n) = K(n/h) /h? (No derivations are required to answer this question.) (c) Can K(a) = exp(%) be used to compute this estimate? Why? (d) In order to ensure a nite-sample estimate f of f with as small a bias as possible, and using the unbiased sample variance estimate 62 of Var(X), indicate which of the following values of it should be used and Why: h1 = 1.06 s N-% h2 = 2.34 s N-% Note: no marks awarded if no explanation is provided; a one-sentence explanation is at! that is required here