> > Dear Professor,
> >
> > In some of the quizzes from last year there are questions along the lines
> > of ???there are x number of balls in a bag number 1 - x. A ball is chosen at
> > at random its number i is noted and then returned to the bag, a second ball
> > is taken and its number j is noted. Calculate the mean and variance of the
> > distribution of k where k = i+j (2 <= k <= 8 
> >
> > I???m just wondering where this is covered in the notes and if there are any
> > worked examples
>

 
This is a variant of the `pair of dice' question.  The difference
is that a pair of dice question produces 2..12 and this produces
2..8.  But it is calculated `from first principles' in the same way.