A total of \(n\) points are dropped on the interval \((0, a)\). Assuming that the points have been dispersed at random [that is, each of them is situated irrespective of the others and is distributed uniformly on \((0, a)\) ], find:

(a) the density function of the abscissa of the \(k\) th point on the left;

(b) the joint density function of the abscissas of the \(k\) th and \(m\) th points on the left \((k