5 The discrete random variables \(X\) and \(Y\) are independent with \(X \sim \mathrm {~B} \left( 32 , \frac { 1 } { 2 } \right)\) and \(Y \sim \operatorname { Po } ( 28 )\).
- Find the values of \(\mathrm { E } ( Y - X )\) and \(\operatorname { Var } ( Y - X )\).
- State, with justification, an approximate distribution for \(Y - X\).
- Hence find \(\mathrm { P } ( | Y - X | \geqslant 3 )\).