4. The discrete random variable \(X\) has probability function
$$\mathrm { P } ( X = x ) = \begin{array} { l l }
0.2 , & x = - 3 , - 2
\alpha , & x = - 1,0
0.1 , & x = 1,2 .
\end{array}$$
Find
- \(\alpha\),
- \(\mathrm { P } ( - 1 \leq X < 2 )\),
- \(\mathrm { F } ( 0.6 )\),
- the value of \(a\) such that \(\mathrm { E } ( a X + 3 ) = 1.2\),
- \(\operatorname { Var } ( X )\),
- \(\operatorname { Var } ( 3 X - 2 )\).