- The probability generating function of the discrete random variable \(X\) is given by
$$G _ { x } ( t ) = k \left( 3 + t + 2 t ^ { 2 } \right) ^ { 2 }$$
- Show that \(\mathrm { k } = \frac { 1 } { 36 }\)
- Find \(\mathrm { P } ( \mathrm { X } = 3 )\)
- Show that \(\operatorname { Var } ( \mathrm { X } ) = \frac { 29 } { 18 }\)
- Find the probability generating function of \(2 \mathrm { X } + 1\)
\section*{Q uestion 6 continued}
\section*{Q uestion 6 continued}
\section*{Q uestion 6 continued}