### 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 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.