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The diagram shows the graph of the probability density function, f , of a random variable \(X\) which takes values between 0 and 4 only. Between these two values the graph is a straight line.
Show that \(\mathrm { f } ( x ) = k x\) for \(0 \leqslant x \leqslant 4\), where \(k\) is a constant to be determined.
Hence, or otherwise, find \(\mathrm { E } ( X )\).
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The diagram shows the graph of the probability density function, g , of a random variable \(W\) which takes values between 0 and \(a\) only, where \(a > 0\). Between these two values the graph is a straight line.
Given that the median of \(W\) is 1 , find the value of \(a\).
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