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\includegraphics[max width=\textwidth, alt={}, center]{4a5f9f7e-b045-4c6f-8bda-6c4067668da2-04_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.
- Show that \(c = \frac { 2 } { 3 }\).
- Find \(\mathrm { P } ( X > 2 )\).
- Calculate \(\mathrm { E } ( X )\).