The continuous random variable \(X\) has probability density function \(\mathrm { f } ( x )\), shown in the diagram, where \(k\) is a constant.
\includegraphics[max width=\textwidth, alt={}, center]{f4fa6add-5860-4c88-bb70-f3edd9b22211-12_511_1096_351_351}
Find \(\mathrm { P } ( X < 10 k )\)
Show that \(k = \frac { 1 } { \pi }\)
Find, in terms of \(\pi\), the values of
\(\mathrm { E } ( X )\)
\(\operatorname { Var } ( X )\)
Circles are drawn with area \(A\), where
$$A = \pi \left( X + \frac { 2 } { \pi } \right) ^ { 2 }$$