Let (Xn)nen be a sequence of i.i.d. random variables with E[X] = R and Var[X] = 0 (0, 0). We define We define = n n i=1 X; (sample mean), $2 = n (a) Show that E[Xn] = , Var[Xn] P (b) Show that S2 . n x+u (c) (c) Assume furthermore that exists. Show that (d) Conclude that 1 n n i=1 = n 1 n (X; - Xn) (sample variance). n 1 - i=1 and E[S2] = 0. = E[(X )] (4,) (the centered fourth moment of X) - - - ) - 02 d(0, (c) - 04). nxx n n (S22 - 0) d N(0, (c) 04). - n