2. The continuous random variable \(X\) is uniformly distributed over the interval \([ \alpha , \beta ]\) where \(\beta > \alpha\)
Given that \(\mathrm { E } ( X ) = 8\)
- write down an equation involving \(\alpha\) and \(\beta\)
Given also that \(\mathrm { P } ( X \leqslant 13 ) = 0.7\)
- find the value of \(\alpha\) and the value of \(\beta\)
- find \(\operatorname { Var } ( X )\)
- find \(\mathrm { P } ( 5 \leqslant X \leqslant 35 )\)