2 The probability generating function of the discrete random variable \(X\) is \(\frac { \mathrm { e } ^ { 4 t ^ { 2 } } } { \mathrm { e } ^ { 4 } }\). Find
- \(\mathrm { E } ( X )\),
- \(\mathrm { P } ( X = 2 )\).
\(3 X _ { 1 }\) and \(X _ { 2 }\) are continuous random variables. Random samples of 5 observations of \(X _ { 1 }\) and 6 observations of \(X _ { 2 }\) are taken. No two observations are equal. The 11 observations are ranked, lowest first, and the sum of the ranks of the observations of \(X _ { 1 }\) is denoted by \(R\).