1 The independent random variables \(X\) and \(Y\) have the distributions \(\mathrm { N } \left( 10 , \sigma ^ { 2 } \right)\) and \(\operatorname { Po } ( 2 )\) respectively. The random variable \(S\) is given by \(S = 5 X - 2 Y + c\), where \(c\) is a constant.
It is given that \(\mathrm { E } ( S ) = \operatorname { Var } ( S ) = 408\).

1. Find the value of \(c\) and show that \(\sigma ^ { 2 } = 16\).
2. Find \(\mathrm { P } ( X \geqslant \mathrm { E } ( Y ) )\).