Let X be a continuous random variable with PDF
\({f_x}\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {{x^2}\left( {kx + \frac{3}{2}} \right)\;\;\;\;\;\;\;0 < x \le 1}\\ {0\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;otherwise} \end{array}} \right.\)
The value of \(var\left( {\frac{1}{x}} \right)\) is ____1
\(\frac{{71}}{{144}}\)
2
\(\frac{{71}}{{72}}\)
3
\(\frac{{71}}{{36}}\)
4
\(\frac{{71}}{{54}}\)