I have this question here that I could use some help with.
Let $X_1$, $X_2$, . . . be a sequence of random variables such that $P(X_n=\frac{k}{n})=\frac{1}{n}$, for $k=1,2,...,n$
Determine the limit distribution of $X_n$ as $n\rightarrow \infty$.
Now I think that if I could find $f_X(x)$ and $F_X(x)$ for $X_n$ then I would have no problem. I guess then you can just use limits or the characteristic function to find the limit distribution. But I'm having a hard time finding them. Anyone that has some idea where to start?
Thanks!