Question: Problem 2- 15 POINTS TOTAL. Let In be an I.I.D. Bernoulli process with a parameter p. Consider the construction of a sum process as follows:

Problem 2- 15 POINTS TOTAL. Let In be an I.I.D. Bernoulli process with a parameter p. Consider the construction of a sum process as follows: n Sn = Ii = Sn-1+ In, for n E Z and So = 0 i=1 Since we are summing a collection of Bernoulli's, the result is distributed Binomial. P[Sn = k] = ( )p*(1 -p)"-k for k E [0, n] . 5 POINTS Show that P(Sn = j, Sm = i) * P(S, = j) . P(Sm = 2) . 5 POINTS Determine P(Sn = j\\Sm = i), where n > m. . 5 POINTS Is Sn a Markov process? Why or Why not

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