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seen Jun 26 '12 at 15:00

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