Tom Chen

 9 A sum of Fibonacci numbers 6 The upper bound of $\lim \limits_{n\to\infty} \sum \limits_{i=1}^n e^{-i}\sqrt{i}$? 5 Dice: Rolling at least N successes where number of succeses vary by dice value 5 Functional equation $(n+1) f(n+1)= (a n+b) f(n)$ for $n=0,1,…$ 4 Is this matrix positive semidefinite? $M_{ij} = \sqrt{|x_i+x_j|} - \sqrt{|x_i-x_j|}$ where $x_i$'s are reals

### Reputation (3,295)

 +20 Why is the statistic $t=r \sqrt{\frac{n-2}{1-r ^2}} \approx t (n-2)$? +40 Is this matrix positive semidefinite? $M_{ij} = \sqrt{|x_i+x_j|} - \sqrt{|x_i-x_j|}$ where $x_i$'s are reals +10 Conditional distribution of subvector of a Dirichlet random variable +10 Does sampling a distribution linearly at random preserve that distribution?

### Questions (28)

 5 A ridiculously fast way to find fixed points of the logistic function? 3 Redux: An interesting four sum inequality (feat. probability) 3 Vandermonde-type convolution with geometric term 2 An interesting stopping time problem using PGF's 2 Sums of Cauchy distributions and their conditional distribution

### Tags (138)

 36 probability × 36 12 probability-distributions × 14 23 inequality × 20 11 functional-analysis × 4 20 real-analysis × 12 11 limits × 4 18 sequences-and-series × 10 10 summation × 4 14 probability-theory × 13 9 linear-algebra × 8

### Bookmarks (86)

 232 “Integral Milking” 90 If $S$ is an infinite $\sigma$ algebra on $X$ then $S$ is not countable 89 Contest problem: Show $\sum_{n = 1}^\infty \frac{n^2a_n}{(a_1+\cdots+a_n)^2}<\infty$ s.t., $a_i>0$, $\sum_{n = 1}^\infty \frac{1}{a_n}<\infty$ [closed] 85 Polynomials such that roots=coefficients 74 Stirling's formula: proof?