- The random variable \(X\) has probability function
$$\mathrm { P } ( X = x ) = \frac { x ^ { 2 } } { k } \quad x = 1,2,3,4$$
- Show that \(k = 30\)
- Find \(\mathrm { P } ( X \neq 4 )\)
- Find the exact value of \(\mathrm { E } ( X )\)
- Find the exact value of \(\operatorname { Var } ( X )\)
Given that \(Y = 3 X - 1\)
- find \(\mathrm { E } \left( Y ^ { 2 } \right)\)