Triangle Experiment

Stick
Scatterplot
Distribution graph

Description

The triangle experiment is a random experiment in which two points are chosen at random in the interval \([0, 1]\); random variable \(X\) denotes the first point chosen and \(Y\) denotes the second point chosen. Random variables \(A\), \(B\), and \(C\) are the sides of the stick pieces, in increasing order. Finally, random variable \(U\) gives the type of triangle that can be formed from the three pieces:

  1. \(U = 0\): the pieces do not form a triangle.
  2. \(U = 1\): the pieces form an obtuse triangle.
  3. \(U = 2\): 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:

  1. \(U = 0\) consists of the 4 outer regions.
  2. \(U = 1\) consists of the 6 middle regions.
  3. \(U = 2\) 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.