3
\includegraphics[max width=\textwidth, alt={}, center]{ec7cab36-683b-4022-9cac-fb3b4e64778a-04_332_1100_260_520} A random variable \(X\) takes values between 0 and 3 only and has probability density function as shown in the diagram, where \(c\) is a constant.

1. Show that \(c = \frac { 2 } { 3 }\).
2. Find \(\mathrm { P } ( X > 2 )\).
3. Calculate \(\mathrm { E } ( X )\).