mike
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 Mar 28 awarded Yearling Mar 28 awarded Yearling Sep 24 awarded Autobiographer Mar 28 awarded Yearling Feb 20 comment Expected wait time for multiple near-simultaneous failures days${}{}{}{}{}$ Feb 19 answered Expected wait time for multiple near-simultaneous failures Feb 18 comment Expected minimum of a finite random walk. for a mean 0 random walk the minimum is not finite, and in general it is hard, and probably unsatisfactory, but you could find a discussion in Spitzer's random walk book, or, I think, Feller Vol 2. Feb 13 comment How to find a function in $L_{2}(0,\infty)$ but not $L_{q}(0,\infty)$, $q\neq 2$ do the cases q > 2 and q < 2 seperately and add the results. Feb 7 answered Cutting time out of a Poisson process Feb 4 comment $\mathbb L^1 +$ a.s. convergence of sequence $(X_n)$ does not imply $\sup(x_n)$ is integrable the typesetting on that last bit is not what I intended, but I'll leave it unless it confuses you. Feb 4 answered $\mathbb L^1 +$ a.s. convergence of sequence $(X_n)$ does not imply $\sup(x_n)$ is integrable Feb 3 comment Relatively compact subspace exercise. you've left out p, which i believe goes here:$\int_0^1|f'(t)|^pdt$ Feb 3 comment $L\log L$ and $L^p$ embedding "Does this embedding hold on for instance, the whole of R n , " $\rightarrow$ Does this embedding hold on for instance, the whole of R n , with lebesgue measure . It does not. In $\mathbb R^1$. e.g., take any sequence $a_n > 0$ that is square summable but not LlogL summable, $a_n = 1/n$ will do. Then take the step function equal to $a_n, n < x < n+1$ and $0$ elsewhere. Jan 30 comment Cardinality of random points in the real number line this is probably not what you have in mind: run a two state markov process with stationary initial distribution $= (\frac 12, \frac 12)$. Flip a coin to decide what stat you start in, run the process forward & backward, and label the real according to the state of the process. I'm guessing you want something more like i.i.d. labelling. Jan 30 comment Random determinant problem the expected determinant is a linear combination with positive weights of determinants each of which is increasing, this is literally true of the distribution of the random guys has finite support, and is true in the sense of being a limit of such guys, or an intergral of them, if you prefer. Jan 30 comment Proving Linear Independence of Gaussian Functions in case your still interested, suppose they are ordered by decreasing $\mu_i$. It is east to show that $\lim_{x \rightarrow \infty} e^{x^2}e^{-2 \mu_1 x} \times$ your function $= a_1e^{\mu_1^2}$ which then has to be 0. Jan 29 comment Proving Linear Independence of Gaussian Functions multiply by $e^{x^2}$ and consider growth rate as $x \rightarrow \infty$. It will be determinined by largest $\mu_i$, whose coefficient must therefore be 0. Get rid of it & repeat. Jan 28 answered Random determinant problem Jan 27 comment How prove this $\frac{1}{b_{k+1}b_{k+2}}+\frac{1}{b_{k+2}b_{k+3}}+\cdots+\frac{1}{b_{2k}b_{2k+1}}>\frac{1}{12345},$ I'm guessing first use arithmetic/geometric then convexity of $1/x^2$ then your idea. Jan 25 comment Random determinant problem I'd be happy too, but what does $^H$ mean ? No sense in running off if its not what I'm guessing.