The continuous random variable $$\(X\)$$ has probability density function f given by $$\[ \mathrm{f}(x)= \begin{cases}k x^{3} & 0 \leqslant x< 1 \\ k(5-x) & 1 \leqslant x \leqslant 5 \\ 0 & \text { otherwise }\end{cases} \]$$ where $$\(k\)$$ is a constant. Find the cumulative distribution function of $$\(X\)$$. ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ . ........................................................................................................................................................ .

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