The continuous random variable $X$ has a probability density function (pdf) given by $$f(x) = \begin{cases} 1 - \frac{1}{2} x & \mbox{ for } 0 \le x \le 2 \\ 0 & \mbox{ otherwise } \\ \end{cases}$$

Part(a) Find the value of $q$ such that $P(X < q) = \frac{1}{4}.$ Give your answer as a decimal correct to 3 decimal places.

Part(b) Find Var($X$), correct to 2 decimal places.

Part(c) Find the value of $c$ correct to one decimal place given that $E(X+c)=4E(X−c)$.

Part(d) Find the median of $X$, correct to 2 decimal places.

Part(e) Find $E( \sqrt{ X } )$, correct to 2 decimal places.

Part(f) Two independent observations of $X$ are taken. Find the probability correct to 2 decimal places that one is less than $\frac{1}{2}$ and the other is greater than $\frac{1}{2}$.