Random Walk Experiment

Walk graph
Distribution graph

Description

The experiment consists of running the symmetric random walk process on the discrete time interval $$\{0, 1, \ldots, n\}$$. That is, the process starts at position 0 and at each time step, independently of the past, the postion either increases by 1 or decreases by 1, each with probability $$\frac{1}{2}$$. The random variables of interest are

The path of the random walk is shown in red in the left graph on each update. Red dots are shown at $$(n, X)$$, $$(0, Y)$$, and $$(Z, 0)$$. The value of each of the three random variables is recorded in the data table on each update. Any of the three variables can be selected from the list box. The probability density function and moments of the selected variable are shown in blue in the distribution graph and are recorded in the distribution table. On each update, the empirical density function and moments are shown in red in the distribution graph and are recorded in the distribution table. The number of steps $$n$$ can be varied with the input control.