The diagram shows the graph of the probability density function f of a random variable $$\(X\)$$. Between $$\(x=0\)$$ and $$\(x=a\)$$ the graph consists of a straight line through $$\(O\)$$ with gradient $$\(k\)$$, where $$\(k\)$$ and $$\(a\)$$ are positive constants. Elsewhere $$\(\mathrm{f}(x)=0\)$$. It is given that the median of $$\(X\)$$ is $$\(\sqrt{2}\)$$. Find the value of $$\(\mathrm{E}(X)\)$$. . . . . . . . . . . . . .

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