7. The continuous random variable \(X\) is uniformly distributed over the interval \([ a , b ]\)
- Find an expression, in terms of \(a\) and \(b\), for \(\mathrm { E } ( 3 - 2 X )\)
- Find \(\mathrm { P } \left( X > \frac { 1 } { 3 } b + \frac { 2 } { 3 } a \right)\)
Given that \(\mathrm { E } ( X ) = 0\)
- find an expression, in terms of \(b\) only, for \(\mathrm { E } \left( 3 X ^ { 2 } \right)\)
Given also that the range of \(X\) is 18
- find \(\operatorname { Var } ( X )\)
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