Question: 6. (10 points) Let (S,)neo be a simple random walk starting in 0 (i.e. So = 0) with p = 0.4 and q=1-p =0.6. Compute

6. (10 points) Let (S,)neo be a simple random walk starting in 0 (i.e. So = 0) with p = 0.4 and q=1-p =0.6. Compute explicitly following quantities: (i) P[S2 = -2, S5 = -1], (ii) P[S2 = -2, S4 = 0, Ss = 2], (ii) P[Is 0 : S, = k} for all ke Z. (iv) E[Ma], where My = maxi=0...,3 Si

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