If we have a piecewise function defined as
$f(x) = \begin{cases} 1, & \text{0 $\le$ $x$ $\le$ 1} \\ 0, & \text{otherwise} \end{cases}$
Explain how the convolution of $f$ with itself for $n$ times i.e. $(f*f*f.......*f)$ $n$ times might begin to look like bell curve of the central limit theorem. I have no idea how to proceed. Any help would be appreicated.
As I have no idea of your background, I will do as @Ian has done : try to give you an intuitive feeling of what is "behind the curtain".
$f$ is the pdf of a uniformly distributed Random Variable $X$ which is simulated by a call to a (pseudo) random number generator "rand" (or "Random" or ... depending on the language you use).
Have you seen that the pdf of a sum of independant identically distributed (i.i.d.) random variables is the convolution of their pdfs ?
If you have, say, four independent variables $X_k, (k=1 \cdots 4)$, have you tried to plot an histogram, of 100,000 sums $X_1+X_2$ (100,000 times rand+rand) ? (This is the first thing I ask to my students to do). You should observe that, though not gaussian-shaped, it is no longer uniformly distributed on $(0,2)$. You may even observe that it looks like a tent).
Then proceed to sums $X_1+X_2+X_3$ which begin to take a bell-curve shape on $(0,3)$, and so on...