Please explain the last sentence: "If t is odd, Xt and Xt-1 is obviously dependent". How can we show that Xt and Xt-1 are dependent?

Let ( Z, ) be IID N(0, 1) noise and define if t is even, X, = 1(23, - 1)/V2, ift is odd. Show that (X,] is WN(0, 1) but not iid(0, 1) noise. Solution First we show that {X, : te Z) is WN (0, 1). For t even we have EX.] = E[Z.] = 0 and for t odd EX.] = E [ZZ-1 - 1] -EIZZ_, - 1) = 0. Next we compute the ACVF. If t is even we have yx (t, t) = E[Z?] = 1 and if t is odd V x ( t , t ) = = ( 2 - - 1) - ;BIZ2 1 - 227 1+ 11 -3(3-2+1)=1. If t is even we have and if t is odd Yx (t + 1, 1) = E Ze+1- 2 V2 Clearly Yx (t + h, t) =0 for [h| 2 2. Hence vx (t + h, h ) = 1 if h = 0, 0 otherwise. Thus {Xt : te Z} is WN (0, 1). If t is odd X, and Xt-1 is obviously dependent so {Xt : te Z} is not IID (0, 1)