Suppose that Xk is a sequence of IID Gaussian random variables. Recall that the sample variance is given by

(a) Show that the sample variance can be written as a quadratic form ŝ2 = XTBX and find the corresponding form of the matrix B.
(b) Use the techniques outlined in Section 6.4.2 to show that the characteristic function of ŝ2is

(c) Show that the PDF of ŝ2is that of a chi- square random variable.

Transcribed Image Text:

Pi 2 (4-il)2 where μ 71 k 1