2. The distance, in metres, a novice tightrope artist, walking on a wire, walks before falling is modelled by the random variable \(W\) with cumulative distribution function
$$\mathrm { F } ( w ) = \left\{ \begin{array} { c c }
0 & w < 0
\frac { 1 } { 3 } \left( w - \frac { w ^ { 4 } } { 256 } \right) & 0 \leqslant w \leqslant 4
1 & w > 4
\end{array} \right.$$
- Find the probability that a novice tightrope artist, walking on the wire, walks at least 3.5 metres before falling.
A random sample of 30 novice tightrope artists is taken.
- Find the probability that more than 1 of these novice tightrope artists, walking on the wire, walks at least 3.5 metres before falling.
Given \(\mathrm { E } ( W ) = 1.6\)
- use algebraic integration to find \(\operatorname { Var } ( W )\)
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