Chapter 11.5, Problem 51E

In Exercises 51 and 52, consider another two-dimensional random walk governed by the following conditions.

● Start out from a given street corner, and travel one block north. At each intersection:

● Turn left with probability $\frac{1}{6}$.

● Go straight with probability $\frac{2}{6}\left(=\frac{1}{3}\right)$.

● Turn right with probability $\frac{3}{6}\left(=\frac{1}{2}\right)$.

(Never turn around.)

A Random Walk Using a Random Number Table Use Table 20 to simulate this random walk, For every 1 encountered in the table, turn left and proceed for another block. For every 2 or 3, go straight and proceed for another block. For every 4, 5, or 6, turn right and proceed for another block. Disregard all other digits-that is, 0s, 7s, 8s, and 9s. (Do you see how this scheme satisfies the probabilities given above?) This time, begin at the upper right corner of the table, running down the column 2, 6, 0, and so on, to the bottom. When this column of digits is used up. stop the “walk.” Describe, in terms of distance and direction, where you have ended up relative to your starting point.