Consider a random walk as described in Example 9.13. After one million steps, find the probability that the walk is within 500 steps from the origin.
Random walk. Random walks are fundamental models in physics, ecology, and numerous fields. They have been popularized in finance with applications to the stock market. A particle starts at the origin on the integer number line. At each step, the particle moves left or right with probability 1/2. Find the expectation and standard deviation of the distance of the walk from the origin after n steps.