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Question 4: Random Walks Consider a one-dimensional biased random walk where the probability of moving right = 1/3 and the probability of moving left = 2/3. Suppose that the run length (distance covered in a single time step) is l = 0.5, and that all walkers are at the origin (x = 0) at time t = 0. Let P_n(d) be the probability that a walker is at position d after n time steps. Find the following probabilities, justifying your answer in each case: i. P_4(1.5) ii. P_2(0) iii. P_3(-0.5) iv. P_4(-2) v. P_5(2.5) vi. P_2(2)

          Question 4: Random Walks

Consider a one-dimensional biased random walk where the probability of moving
right = 1/3 and the probability of moving left = 2/3. Suppose that the run length (distance
covered in a single time step) is l = 0.5, and that all walkers are at the origin (x = 0) at time
t = 0.

Let P_n(d) be the probability that a walker is at position d after n time steps. Find the
following probabilities, justifying your answer in each case:

i. P_4(1.5)
ii. P_2(0)
iii. P_3(-0.5)
iv. P_4(-2)
v. P_5(2.5)
vi. P_2(2)

Question 4: Random Walks

Consider a one-dimensional biased random walk where the probability of moving
right = 1/3 and the probability of moving left = 2/3. Suppose that the run length (distance
covered in a single time step) is l = 0.5, and that all walkers are at the origin (x = 0) at time
t = 0.

Let Pn(d) be the probability that a walker is at position d after n time steps. Find the
following probabilities, justifying your answer in each case:

i. P4(1.5)
ii. P2(0)
iii. P3(-0.5)
iv. P4(-2)
v. P5(2.5)
vi. P2(2)

Added by Kyle J.

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