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 Apr 25 comment Number of random values that are recorded as being greater than all previous values I believe the $X_i$ are independent, since $X_i = \mathbf 1_{A_i}$ where $A_i = \{i\text{th trial is a new max}\}$ and the $A_i$ are known to be mutually independent events. (Lemma 1 of A. Renyi (1962), Théorie des éléments saillants d'une suite d'observations, Annales scientifiques de l'Université de Clermont. Mathématiques 8.2.) Feb 13 awarded Yearling Sep 20 comment $\langle X\rangle_t = t?$ "Related". Jul 6 awarded Enlightened Jul 6 awarded Nice Answer May 12 awarded Nice Answer Apr 10 comment Example of pairwise independent random process with expected max load $\sqrt{n}$. Feb 17 comment Solving the integral $\int_{0}^{\infty} \frac{\sin{x}}{x} \ dx = \frac{\pi}{2}$? @Ale: As regards your comment, yes, Fubini is applied correctly as stated in my comment. For each fixed $a$, the associated integral is bounded. Hence, Fubini can be used to compute the integral in two ways. Rearranging gives you a bound for $|\int_0^a \frac{\sin x}{x} - \frac{\pi}{2}|$ as a function of $a$. Then, take $a \to \infty$ to get the result. (Note that some argument like this is necessary since $\frac{\sin x}{x}$ is not integrable on $(0,\infty)$ in the Lebesgue sense.) Hope this helps. Cheers. :-) Feb 13 awarded Yearling Dec 16 awarded Enlightened Dec 16 awarded Nice Answer Sep 30 awarded Explainer Jun 18 comment Does affine equivariance implies shape unbiasedness? Hi @user: The edit is helpful. It doesn't appear to address my remarks on the equivariance definition, though. Cheers. Jun 18 comment Does affine equivariance implies shape unbiasedness? Can you clear up the statement of affine equivariance? Currently none of the operations are well defined (matrix multiplication where dimensions don't match and addition of matrix and vector). What, if any, distributional assumptions on $\mathbf X$ are you making? (Independent rows?) Feb 19 comment Why does this covariance matrix have additional symmetry along the anti-diagonals? @Michael: Please check the timestamps of the edits and comments. Cheers. Feb 16 awarded Nice Answer Feb 13 awarded Yearling Jan 1 comment Inequalities of the quantile function possible duplicate of Quantile function properties Dec 29 comment Triple Euler sum result $\sum_{k\geq 1}\frac{H_k^{(2)}H_k }{k^2}=\zeta(2)\zeta(3)+\zeta(5)$ Please post the symbolic input you entered. Dec 22 comment $\int_{t=-\infty}^x (G(t)-F(t))\mbox{d}t\geq 0\forall x$ and $\frac{\mbox{d}F(t)}{\mbox{d}G(t)}$ increasing $\Longrightarrow G(x)\geq F(x)\forall x$? Are $1-$ and $2-$ supposed to be item identifiers in a list? If so, the way you have it typeset makes it very easy to confuse it with something very different!