Description

In the triangle experiment, 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:

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

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

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

When the experiment runs, the random point \((X, Y)\) is shown as a red dot in the scatterplot, and the variables \(X\), \(Y\), \(A\), \(B\), \(C\), and \(U\) are recorded in the data table. The distribution of \(U\) is described in the distribution graph and table.