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\includegraphics[max width=\textwidth, alt={}, center]{2fefee17-50bb-4375-80f6-7e4bc2606492-04_405_789_260_676}
The diagram shows the graph of the probability density function, f , of a random variable \(X\).
- Find the value of the constant \(k\).
- Using this value of \(k\), find \(\mathrm { f } ( x )\) for \(0 \leqslant x \leqslant k\) and hence find \(\mathrm { E } ( X )\).
- Find the value of \(p\) such that \(\mathrm { P } ( p < X < 1 ) = 0.25\).