Square root transformation (Y = √X)

3 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 3 } { 16 } ( 2 - \sqrt { x } ) & 0 \leqslant x < 1
\frac { 3 } { 16 \sqrt { x } } & 1 \leqslant x \leqslant 9
0 & \text { otherwise } \end{cases}$$

1. Find \(\mathrm { E } ( X )\).
   The random variable \(Y\) is such that \(Y = \sqrt { X }\).
2. Find the probability density function of \(Y\).

6 The continuous random variable \(X\) has probability density function f given by $$f ( x ) = \begin{cases} \frac { 1 } { 80 } \left( 3 \sqrt { } x - \frac { 8 } { \sqrt { } x } \right) & 4 \leqslant x \leqslant 16
0 & \text { otherwise } \end{cases}$$

1. Find the distribution function of \(X\).
   The random variable \(Y\) is defined by \(Y = \sqrt { } X\).
2. Find the probability density function of \(Y\).