I am trying to resolve the following problem:
$\{X_n\}$ is a succession of random variables with probability function:
$$ \begin{array}{|c|c|c|c|} \hline X_n & 2 - \frac{1}{n} & 3 - \frac{1}{n} & 4 - \frac{1}{n} \\ \hline p(x) & \frac{1}{3} & \frac{1}{3} & \frac{1}{3} \\ \hline \end{array} $$
Can the central limit theorem be applied to this succession? Eplain.
My main problem is that I do not understand the central limit theory and therefore I do not know what I have to prove.
Could anyone assist me in understanding the concept or at least what calculations I need to do to prove this theorem?