3. The discrete random variable \(X\) has probability distribution
$$\mathrm { P } ( X = x ) = \frac { 1 } { 5 } \quad x = 1,2,3,4,5$$
- Write down the name given to this distribution.
Find
- \(\mathrm { P } ( X = 4 )\)
- \(\mathrm { F } ( 3 )\)
- \(\mathrm { P } ( 3 X - 3 > X + 4 )\)
- Write down \(\mathrm { E } ( X )\)
- Find \(\mathrm { E } \left( X ^ { 2 } \right)\)
- Hence find \(\operatorname { Var } ( X )\)
Given that \(\mathrm { E } ( a X - 3 ) = 11.4\)
- find \(\operatorname { Var } ( a X - 3 )\)