The experiment consists of running the Brownian bridge process \( \boldsymbol{Y} = \{Y_t: t \in [0, 1] \} \), which is obtained from the standard Brownian motion process \( \boldsymbol{X} = \{X_t: t \in [0, 1]\} \) by conditioning on the event \( X(1) = 0 \). On each run, the path is shown in the top graph. The random variable of interest is the position \( Y_t \) at time \( t \in [0, 1] \), which has the normal distribution with mean 0 and standard deviation \( \sqrt{t (1 - t)} \).
On each run, the value of the variable is recorded in the data table, and the point \( (t, Y_t) \) is shown as a red dot in the path graph. The probability density function and moments, and the empirical density function and moments of \(Y_t\), are shown in the distribution graph amd in the distribution table. The parameter \( t \) can be varied with the input control.