Two points are chosen at
random in the interval [0, 1]; X denotes the first point chosen and Y denotes
the second point chosen. Random variable U gives the type of triangle that can
be formed from the three sub-intervals:
- U = 0: the pieces do not form a triangle.
- U = 1: the pieces form an obtuse triangle.
- U = 2: the pieces form an acute triangle.
The first picture box shows the outcome of the experiment
graphically. On each update, the cut points X and Y are shown as red dots, and
the triangle is sketched when U = 1 or U = 2. The second picture box shows the
sample space and the three events of interest:
- U = 2 consists of the 2 interior regions.
- U = 1 consists of the 6 middle regions.
- U = 0 consists of the outer regions.
On each run, (X, Y) is shown as a red dot in the
scatterplot, and is recorded in the first table on each update The probability
density function of U is shown in blue in the graph box and is recorded in the
graph table. On each update, the empirical density of U is shown in red in the
graph box and is recorded in the graph table. Additionally, the value of U is
recorded in the first table on each update. |
An applet freely
available from