7. The random variable \(y\) has probability density function \(\mathrm { f } ( y )\) given by $$\mathrm { f } ( y ) = \left\{ \begin{array} { c c } k y ( a - y ) & 0 \leq y \leq 3
0 & \text { otherwise } \end{array} \right.$$ where \(k\) and \(a\) are positive constants.

1. 1. Explain why \(a \geq 3\)
   2. Show that \(k = \frac { 2 } { 9 ( a - 2 ) }\) Given that \(\mathrm { E } ( Y ) = 1.75\)
2. Find the values of a and k .
3. Write down the mode of Y