The continuous random variable $$\(X\)$$ has probability density function where $$\(k\)$$ and $$\(a\)$$ are constants. It is known that $$\(\mathrm{P}(X< 4)=\frac{31}{45}\)$$ (a) Find the exact value of $$\(k\)$$ (4) (b) (i) Find the exact value of $$\(a\)$$ (ii) Find the exact value of $$\(\mathrm{P}(0 \leqslant X \leqslant 5.5)\)$$ (3) (c) Specify fully the cumulative distribution function of $$\(X\)$$ (6)

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