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) Recall that the simple random walk is just a Markov chain on the integers where we move from j to j+1 with probability, and from j to j-1 with probability: 2., Find P(Xn+1 =j+1| Xn = j) = 2 1 P(Xn+1 =j-1 | Xn = j) = 2/2 P(Xn+1 = m | Xn = j) = 0 ifm #j+1 or j - 1. (a) P(X+1 = 2 | X, = 0) (i.e. the probability of going from 0 to 2 in one-step) (b) P(X+1 = 2 | X,,= 1) (i.e. the probability of going from 1 to 2 in one-step) (c) P(Xn+2 = 2 | X₁ = 2) (i.e. the probability of going from 2 to 2 in two-steps)

) Recall that the simple random walk is just a Markov chain on the integers where we move from j to j+1 with probability, and from j to j-1 with probability: 2., Find P(Xn+1 =j+1| Xn = j) = 2 1 P(Xn+1 =j-1 | Xn = j) = 2/2 P(Xn+1 = m | Xn = j) = 0 ifm #j+1 or j - 1. (a) P(X+1 = 2 | X, = 0) (i.e. the probability of going from 0 to 2 in one-step) (b) P(X+1 = 2 | X,,= 1) (i.e. the probability of going from 1 to 2 in one-step) (c) P(Xn+2 = 2 | X₁ = 2) (i.e. the probability of going from 2 to 2 in two-steps)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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2. ) Recall that the simple random walk is just a Markov chain on the integers where we move from j to j+1 with probability, and from j to j-1 with probability: . Find 1 P(Xn+1 =j+1| Xn = j) = 2 1 P(Xn+1 =j-1 | Xn = j) = ²/ P(Xn+1 = m | Xn = j) = 0 ifm #j+1 or j - 1. (a) P(Xn+1 = 2 | X, = 0) (i.e. the probability of going from 0 to 2 in one-step) (b) P(X+1 = 2 | X,,= 1) (i.e. the probability of going from 1 to 2 in one-step) (c) P(Xn+2= 2 | X, = 2) (i.e. the probability of going from 2 to 2 in two-steps)
Transcribed Image Text:2. ) Recall that the simple random walk is just a Markov chain on the integers where we move from j to j+1 with probability, and from j to j-1 with probability: . Find 1 P(Xn+1 =j+1| Xn = j) = 2 1 P(Xn+1 =j-1 | Xn = j) = ²/ P(Xn+1 = m | Xn = j) = 0 ifm #j+1 or j - 1. (a) P(Xn+1 = 2 | X, = 0) (i.e. the probability of going from 0 to 2 in one-step) (b) P(X+1 = 2 | X,,= 1) (i.e. the probability of going from 1 to 2 in one-step) (c) P(Xn+2= 2 | X, = 2) (i.e. the probability of going from 2 to 2 in two-steps)
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