5. The random variable \(R\) is defined as \(R = X + 4 Y\) where \(X \sim \mathrm {~N} \left( 8,2 ^ { 2 } \right) , Y \sim \mathrm {~N} \left( 14,3 ^ { 2 } \right)\) and \(X\) and \(Y\) are independent. Find

1. \(\mathrm { E } ( R )\),
2. \(\operatorname { Var } ( R )\),
3. \(\mathrm { P } ( R < 41 )\) The random variables \(Y _ { 1 } , Y _ { 2 }\) and \(Y _ { 3 }\) are independent and each has the same distribution as \(Y\). The random variable \(S\) is defined as $$S = \sum _ { i = 1 } ^ { 3 } Y _ { i } - \frac { 1 } { 2 } X$$
4. Find Var (S).