4
votes
1answer
269 views

Distribution function for divisors of an Integer

For a fixed $n$, let $D_n(x) = \{ d|n : d \leq x \}$ . We assume here $p \leq x \leq n/p$, where $p$ is the smallest prime factor of $n$. For example if $n = p^i$ for some prime $p$ then $D_n(x) ...
4
votes
2answers
1k views

Convergence of moments implies convergence to normal distribution

I have a sequence $\{X_n\}$ of random variables supported on the real line, as well as a normally distributed random variable $X$ (whose mean and variance are known but irrelevant). I know that the ...