- The random variable \(X\) has probability function
$$\mathrm { P } ( X = x ) = \frac { ( 2 x - 1 ) } { 36 } \quad x = 1,2,3,4,5,6$$
- Construct a table giving the probability distribution of \(X\).
Find
- \(\mathrm { P } ( 2 < X \leqslant 5 )\),
- the exact value of \(\mathrm { E } ( X )\).
- Show that \(\operatorname { Var } ( X ) = 1.97\) to 3 significant figures.
- Find \(\operatorname { Var } ( 2 - 3 X )\).