5 The continuous random variable \(X\) has cumulative distribution function
$$\mathrm { F } ( x ) = \left\{ \begin{array} { c l }
0 & x \leq 1
\frac { 1 } { 10 } x - \frac { 1 } { 10 } & 1 < x \leq 6
\frac { 1 } { 90 } x ^ { 2 } + \frac { 1 } { 10 } & 6 < x \leq 9
1 & x > 9
\end{array} \right.$$
5
- Find the probability density function \(\mathrm { f } ( x )\)
5 - Show that \(\operatorname { Var } ( X ) = \frac { 6737 } { 1200 }\)
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