Step 1	\({l_0}\, = 2.500{(64 – 0,8(0))^{\frac{1}{3}}}\) \({l_0}\, = 10.000\)
Step 2	\(E[X]\, = \int\limits_0^{80} {\frac{{{l_{0 + t}}}}{{{l_0}}}} dt\) \(E[X] = \,\frac{{\int\limits_0^{80} {2.500{{(64 – 0,8x)}^{\frac{1}{3}}}} }}{{10.000}}\,\) \(E[X] = \,\frac{{2.500\frac{3}{4}\left( {\frac{{10}}{8}} \right)\left[ {{{(64 – 0,8(0))}^{\frac{4}{3}}} – {{(64 – 0,8(80))}^{\frac{4}{3}}}} \right]}}{{10.000}}\) \(E[X] = \frac{{600.000}}{{10.000}}\) \(E[X] = 60\)
Step 3	\(E[{X^2}]\,\, = 2\int\limits_0^{80} {x\frac{{{l_{0 + t}}}}{{{l_0}}}} dt\,\) \(E[{X^2}] = \,\frac{{2\int\limits_0^{80} {x\,\,\left[ {2.500{{(64 – 0,8x)}^{\frac{1}{3}}}} \right]} dt}}{{10.000}}\,\,\) \(E[{X^2}] = \,4.114,285711\)
Step 4	\(Var[X] = E[{X^2}]\,\, – \,E{[X]^2}\) \(Var[X] = 4.114 – {60^2}\) \(Var[X] = 514\)
Maka	\(Var[X] – E{[X]^2} = 514 – {60^2}\) \(Var[X] – E{[X]^2} = – 3.086\)
Jawaban	Anulir