2. Let Xi be a sequence of iid random variables and m(t1, . .., t), where k > 1 is fixed, be a measurable function of its components. Let Sn = In 2j=1 Yj, where Yj = m(Xj, Xit1, . .., Xith), j = 1, 2, ... Show that Y; is a a-mixing sequence. Find the limiting distribution of Sn, assuming EY1 = 0, EY1 2+ 0. Note: when you use the decomposition given in class for a a-mixing sequence, you may assume vt is stationary and n E( v? | Ft-1) - 02 n t= 1 for some of to be specified. The other components, including the validity of the decom- position, need to be verified.2. Let Xi be a sequence of iid random variables and m(t1, . .., t), where k > 1 is fixed, be a measurable function of its components. Let Sn = In 2j=1 Yj, where Yj = m(Xj, Xit1, . .., Xith), j = 1, 2, ... Show that Y; is a a-mixing sequence. Find the limiting distribution of Sn, assuming EY1 = 0, EY1 2+ 0. Note: when you use the decomposition given in class for a a-mixing sequence, you may assume vt is stationary and n E( v? | Ft-1) - 02 n t= 1 for some of to be specified. The other components, including the validity of the decom- position, need to be verified