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 Yearling
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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 $\sqrt{n}$.
A curiously related question posted on MO at about the same time.
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!