Two-Dimensional Brownian Motion

Description

The experiment consists of running a two-dimensional Brownian motion process \( \{(X_s, Y_s): 0 \le s \le t\} \) on the interval \( [0, t] \). Thus, \( \{X_s: s \in [0, \infty)\} \) and \( \{Y_s: s \in [0, \infty)\} \) are independent standard Brownian motions. On each run, the sample path is shown in the first graph in green, with the final position \((X_t, Y_t)\) as a red dot. The values of \(X_t\) and \(Y_t\) are recorded in the data table. The probability density functions and moments, and the empirical density functions and moments of \(X_t\) and \(Y_t\), are shown in the two distribution graphs and given in the two distribution tables. The time parameter \( t \) can be varied with the input control.