The continuous random variable $$\(X\)$$ has a probability density function given by where $$\(k\)$$ is a positive constant. (a) Sketch $$\(\mathrm{f}(x)\)$$ for all values of $$\(x\)$$ (2) (b) Show that $$\(k=\frac{1}{6}\)$$ (2) (c) Specify fully the cumulative distribution function $$\(\mathrm{F}(x)\)$$ of $$\(X\)$$ (7) Given that $$\(\mathrm{E}(X)=\frac{61}{12}\)$$ (d) find $$\(\mathrm{P}(X> \mathrm{E}(X))\)$$ (2) (e) Describe the skewness of the distribution, giving a reason for your answer. (2)

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