Triangle Experiment

]> Triangle Experiment

Description

The triangle experiment is a random experiment in which two points are chosen at random in the interval $01$ ; random variable $X$ 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 picture box shows the outcome of the experiment graphically. On each update, the triangle is sketched when $U 1$ or $U 2$ and the stick is shown broken when $U 0$ .

The scatterplot shows the sample space and the three events of interest:

$U 0$ consists of the outer regions.
$U 1$ consists of the 6 middle regions.
$U 2$ consists of the 2 interior regions.

On each run, $X Y$ is shown as a red dot in the scatterplot, and is recorded in the record table on each update

The probability density function of $U$ is shown in blue in the distribution graph and is recorded in the distribution table. On each update, the empirical density function of $U$ is shown in red in the distribution box and is recorded in the distribution table. Additionally, the value of $U$ is recorded in the data table on each update.

The Triangle Experiment

Description