6. The continuous random variable \(X\) has (cumulative) distribution function given by $$F ( x ) = \left\{ \begin{array} { c c } 0 & x < 1
1 - \frac { 1 } { x ^ { 4 } } & x \geq 1 \end{array} \right.$$ a. Show that the probability density function of \(Y\), where \(Y = \frac { 1 } { X ^ { 2 } }\), is given by $$g ( y ) = \left\{ \begin{array} { c c } 2 y & 0 < y \leq 1
0 & \text { otherwise } \end{array} \right.$$ b. Find \(\mathrm { E } ( \sqrt [ 3 ] { Y } )\).