3. A rod of length \(2 l\) was broken into 2 parts. The point at which the rod broke is equally likely to be anywhere along the rod. The length of the shorter piece of rod is represented by the random variable \(X\).
- Write down the name of the probability density function of \(X\), and specify it fully.
- Find \(\mathrm { P } \left( X < \frac { 1 } { 3 } l \right)\).
- Write down the value of \(\mathrm { E } ( X )\).
Two identical rods of length \(2 l\) are broken.
- Find the probability that both of the shorter pieces are of length less than \(\frac { 1 } { 3 } l\).