Let \( \bs{X} = \{X_t: t \in [0, \infty)\} \) be standard Brownian motion, and let \( \tau = \min\{t > 0: X_t = 1\} \), the first hitting time to state \( 1 \). This app shows the process \( \bs{Y} = \{Y_s: s \in [0, \infty)\} \) on the interval \( [0, 10] \), where \[ Y_s = \begin{cases} X_s, & s \lt \tau \\ 2 - X_s, & s \ge \tau \end{cases} \] That is, the graph of \( \bs{X} \) is reflected in the line \( x = 1 \) after the process first hits \( 1 \). On each run, the path of \( \bs{X} \) is shown in red, while the reflected portion of the graph of \( \bs{Y} \) is shown in green (whenever \( \tau \lt 10\)). The process \(\bs{Y}\) is also a standard Brownian motion so \( Y_t \) has the normal distribution with mean \( 0 \) and variance \( t \). The hitting time \(\tau\) has the standard Lévy distribution. The values of \(X\), \(Y\), and \(\tau\) (when \(\tau \lt 10)\) are recorded in the data table on each update. The probability density function and moments, and the empirical density function and moments of \(X\), \(Y\), and \(\tau\) are shown in the distribution graphs and recorded in the distribution tables.