7 A continuous random variable \(X\) has the probability density function defined by $$\mathrm { f } ( x ) = \left\{ \begin{array} { c c } x ^ { 2 } & 0 \leqslant x \leqslant 1
\frac { 1 } { 3 } ( 5 - 2 x ) & 1 \leqslant x \leqslant 2
0 & \text { otherwise } \end{array} \right.$$

1. Sketch the graph of f on the axes below.
2. 1. Find the cumulative distribution function, F , for \(0 \leqslant x \leqslant 1\).
   2. Hence, or otherwise, find the value of the lower quartile of \(X\).
3. 1. Show that the cumulative distribution function for \(1 \leqslant x \leqslant 2\) is defined by $$\mathrm { F } ( x ) = \frac { 1 } { 3 } \left( 5 x - x ^ { 2 } - 3 \right)$$
   2. Hence, or otherwise, find the value of the upper quartile of \(X\).
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