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A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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
Transcribed Image Text:A particle executes an unrestricted simple random walk on the line with
p=0.7 and q=0.3. Its position at time n is represented by the
random variable Xn, n = 0, 1,...; Xo = 0.
(a) Calculate the values of the following probabilities.
(i) P(X5 = -2)
(ii) P(X6 = 2)
(b) Calculate the probability that the particle returns to its starting
point for the first time after 8 steps.
(c) After the particle has been moving for some time, it is observed to
be located at the point +3.
(i) Calculate the probability that the particle will ever return to
the origin from the point +3.
(ii)
Calculate the probability that starting from the point +3, the
particle will visit the point +8 without first visiting the origin.
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