The random variable $X$ follows a continuous uniform distribution over the interval $[a - 3, 2a + 3]$ where $a$ is a constant.

The mean of a random sample of size $n$ is denoted by $\overline{X}$.

(a) Show that $\overline{X}$ is a biased estimator of $a$, and state the bias.

Given that $Y = k\overline{X}$ is an unbiased estimator for $a$

(b) find the value of $k$.

A random sample of 10 values of $X$ is taken and the results are as follows

$3 \quad 5 \quad 8 \quad 12 \quad 4 \quad 13 \quad 10 \quad 8 \quad 5 \quad 12$

(c) Hence estimate the maximum value of $X$