7. The continuous random variable \(X\) has probability density function given by $$f ( x ) = \left\{ \begin{array} { c l } 0 & x < 1
\frac { 4 } { x ^ { 5 } } & x \geq 1 \end{array} \right.$$ a. Find the cumulative distribution function, \(F ( x )\), of \(X\).
b. Find the interquartile range of \(X\).
c. Show that the probability density function of \(Y\), where \(Y = \frac { 1 } { X ^ { 2 } }\), is given by $$g ( y ) = \left\{ \begin{array} { c l } 2 y & 0 < y \leq 1
0 & \text { otherwise } \end{array} \right.$$ d. Find the value of \(a\) for which \(\mathrm { E } \left( \frac { 1 } { X ^ { 2 } } \right) = a \mathrm { E } \left( X ^ { 2 } \right)\).