6

6. [Maximum mark: 8]

A continuous random variable $X$ has probability density function
$f(x) = \begin{cases} \frac{1}{5} & 0 \le x < 2 \\ -\frac{x}{30} + \frac{4}{15} & 2 \le x \le 8 \\ 0 & \text{otherwise} \end{cases}$

(a) Find $E(X)$. [3]

(b) Given that $E(c - 2X) = 0$, where $c$ is a constant, determine the value of $c$. [2]

(c) Find the median of $X$. [3]