Random variables \(Y\) and \(X\) are related by \(Y = a + b X\), where \(a\) and \(b\) are constants and \(b > 0\). The standard deviation of \(Y\) is twice the standard deviation of \(X\). The mean of \(Y\) is 7.92 and is 0.8 more than the mean of \(X\). Find the values of \(a\) and \(b\).
Random variables \(R\) and \(S\) are such that \(R \sim \mathrm {~N} \left( \mu , 2 ^ { 2 } \right)\) and \(S \sim \mathrm {~N} \left( 2 \mu , 3 ^ { 2 } \right)\). It is given that \(\mathrm { P } ( R + S > 1 ) = 0.9\).