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Imagine that you have a drunk man moving along the horizontal axis (that stretches from x = to x = +).At time t = 0, his position on this axis is x =...
Imagine that you have a drunk man moving along the horizontal axis (that stretches from x = −∞ to x = +∞).At time t = 0, his position on this axis is x = 0. At each time point t = 1, t = 2, etc., the man moves forward(that is, x(t +1) = x(t)+1) with probability 0.5, backward (that is, x(t +1) = x(t)−1) with probability 0.3,and stays exactly where he is (that is, x(t +1) = x(t)) with probability 0.2.
(a) Calculate the probability of each possible position at t = 2.
(b) If you know the probability of each position at time t, how will you find the probabilities at time t +1?
(a)The probability associated with each of these positionscan be calculated from theprobabilities that we just computed above (for the man’sposition at time t = 1). (b)