I have an integer valued random variable $X_n$ (that takes values in $\{0,1\dots,n\}$) that is a sum of $n$ (dependent) indicator functions. I believe that it converges to some random variable $X$, and I have shown that $E(X_n^k) \rightarrow E(X^k)$ for a $k$ that is relatively small $(k/n \text{ close to 0}) $, and large $k$. $(k/n \text{ close to 1})$. Is there anything I can do with this information without computing other moments which are tough to compute?

  • $\begingroup$ Can you say more about the random variable, in which sense it converges to what, and what are you looking to prove? $\endgroup$ – R_B Apr 7 at 1:31

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