6. In an experiment some children were asked to estimate the position of the centre of a circle. The random variable \(D\) represents the distance, in centimetres, between the child's estimate and the actual position of the centre of the circle. The cumulative distribution function of \(D\) is given by
$$\mathrm { F } ( d ) = \left\{ \begin{array} { c c }
0 & d < 0
\frac { d ^ { 2 } } { 2 } - \frac { d ^ { 4 } } { 16 } & 0 \leqslant d \leqslant 2
1 & d > 2
\end{array} \right.$$
- Find the median of \(D\).
- Find the mode of \(D\).
Justify your answer.
The experiment is conducted on 80 children.
- Find the expected number of children whose estimate is less than 1 cm from the actual centre of the circle.