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\includegraphics[max width=\textwidth, alt={}, center]{189bcf7b-279f-457b-8232-ace7f0c9797f-05_456_668_260_735}
The random variable \(X\) takes values in the range \(1 \leqslant x \leqslant p\), where \(p\) is a constant. The graph of the probability density function of \(X\) is shown in the diagram.
- Show that \(p = 2\).
- Find \(\mathrm { E } ( X )\).