4 The random variable \(X\) has a \(\chi ^ { 2 }\) distribution with \(v\) degrees of freedom. The moment generating function of \(X\) is
$$\mathrm { M } _ { X } ( t ) = ( 1 - 2 t ) ^ { - \frac { 1 } { 2 } v }$$
- Show that \(\mathrm { E } ( X ) = v\).
- Find \(\operatorname { Var } ( X )\).
- Obtain the moment generating function of the sum \(Y\) of two independent \(\chi ^ { 2 }\) random variables, one with 6 degrees of freedom and the other with 8 degrees of freedom.
- Identify the distribution of \(Y\).