9 The continuous random variable \(X\) has probability density function f given by
$$\mathrm { f } ( x ) = \begin{cases} 0 & x < 0 ,
a \mathrm { e } ^ { - x \ln 2 } & x \geqslant 0 , \end{cases}$$
where \(a\) is a positive constant.
- Find the value of \(a\).
- State the value of \(\mathrm { E } ( X )\).
- Find the interquartile range of \(X\).
The variable \(Y\) is related to \(X\) by \(Y = 2 ^ { X }\). - Find the probability density function of \(Y\).