Question

(h) (easy) Let X Fx1.kg, find the kernel of fx(2). (i) (easy) Using 21, 22, ... N (0, 1), find a function g s.t. 9(2,22,...) ~Twhere ke N is a constant.

Answer 1

Answed: he) A kernal is a non-negative real-walued integrable function k For most applications, it is desirable to difine the function to Satisfy two additional requirements: Normalization: k(u) du = 1; Symmetry: K(-u) = K (4) for all values of u. The first requirement ensures that the method of kermal density estimation result in a probability density function the second requirement ensures that the average of the cooresponding distribution is equal to that of the sample used. If k is a kernal, then so is the function defined by K* (u) = 2K (Au), where 270 - This can be used to select a scale that is appropriate for the data- 1.2. Triweight 08 10: 50 05-1

h) Given XNFkika -kitk Kernel of fyl) is, KCM): 35 C1-), 10131 i) Given Zizzi... (011) If z is a standard normal with expected value o u variance 1, then -Z +1 2 g (2) = 1 2 + 1 2 - kao g (2) NiK, KEN is a constant.