1. For independent RVs X1, X2, X3, put S, := E1 Xj, n = 1,2, 3....

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1. For independent RVs X1, X2, X3, put S, := E1 Xj, n = 1,2, 3. Show that Si and S3 are conditionally independent given S2. Assuming for simplicity that the X;'s are integer-valued, this means that, for any integer kj: P(S = k, S3 = ks | S2 = k2) = P(S; = k | S2 = k2) P(S, = ka| S2 = ka). %D NB: This property holds for any Markov chain {S,}; in fact, this is the Markov property. 1. For independent RVs X1, X2, X3, put S, := E1 Xj, n = 1,2, 3. Show that Si and S3 are conditionally independent given S2. Assuming for simplicity that the X;'s are integer-valued, this means that, for any integer kj: P(S = k, S3 = ks | S2 = k2) = P(S; = k | S2 = k2) P(S, = ka| S2 = ka). %D NB: This property holds for any Markov chain {S,}; in fact, this is the Markov property.