4 The discrete random variable \(X\) has moment generating function \(\left( \frac { 1 } { 4 } + \frac { 3 } { 4 } \mathrm { e } ^ { t } \right) ^ { 3 }\).
- Find \(\mathrm { E } ( X )\).
- Find \(\mathrm { P } ( X = 2 )\).
- Show that \(X\) can be expressed as a sum of 3 independent observations of a random variable \(Y\). Obtain the probability distribution of \(Y\), and the variance of \(Y\).