=+8.2. Let Yo, Y ,,... be independent and identically distributed with P[Y ,, = 1] =p, P[Y

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=+8.2. Let Yo, Y ,,... be independent and identically distributed with P[Y ,, = 1] =p, P[Y ,, = 0] = q = 1 - p, p + q. Put X„, = Y ,, + Y„+, (mod2). Show that X0; X1 ,...

is not a Markov chain even though P[ X .. + 1 = jlX ,,-, = i] = P[X.+1 =j]. Does this last relation hold for all Markov chains? Why?

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