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 Jul 2 awarded Curious Jun 25 accepted Show that the variance of this random variable is finite Jun 25 accepted Show these simple inequalities Jun 25 comment Show these simple inequalities @ArturoMagidin Yeah. See my update though. Jun 25 revised Show these simple inequalities added 175 characters in body Jun 25 asked Show these simple inequalities Jun 25 awarded Editor Jun 25 revised Show that the variance of this random variable is finite added 241 characters in body Jun 25 comment Show that the variance of this random variable is finite @JohnEngbers Well, it seems to me that I don't even need the $Var[X]$ to be finite. If I can show that $(\log(1+x))^2 < x$ for all $x > 0$ then it seems I'm basically done, since Var[X] is nothing but $E[X^2] - (E[X])^2$. The problem is showing that inequality. What do you think? Jun 25 accepted Does this multivariate function have only one maximum? Jun 25 accepted Proofreading services for mathematical texts Jun 25 asked Show that the variance of this random variable is finite Jun 18 asked Does this multivariate function have only one maximum? Jun 18 accepted Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? Jun 18 comment Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? This function looks somewhat "unstable" near the origin. What if we assume, in addition, that $f(0,\ldots,0) = 0$ and that the $f$ is smooth enough everywhere (including near the origin)? Does that change anything? Intuitively, it seems to me that this would be the case. But how can we confirm it? Jun 18 comment Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? @LeonidKovalev Also, feel free to just assume that the functions are however smooth we need. Does that validate what leonbloy said? Jun 18 comment Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? @LeonidKovalev Yes, but we don't have this result for each line. We only have it for each line going out from the origin. What about all the other lines in the region? Jun 17 comment Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? @LeonidKovalev If $f$ is concave only in each direction, is it necessarily concave in general? Jun 17 asked Can we say something about the number of local maxima of this function ? Can we prove that it has at most $n−1$ local maxima? May 29 awarded Supporter