Problem

The continuous random variable $X$ is uniformly distributed over the interval $[a, b]$

(a) Find an expression, in terms of $a$ and $b$, for $E(3 - 2X)$

(b) Find $P\left(X > \dfrac{1}{3}b + \dfrac{2}{3}a\right)$

Given that $E(X) = 0$

(c) find an expression, in terms of $b$ only, for $E(3X^2)$

Given also that the range of $X$ is 18

(d) find $\text{Var}(X)$

(Total for Question 7 is 9 marks)