Byron Schmuland
Reputation
28,373
85/100 score
3 58 131
Impact
~875k people reached

 74 Striking applications of integration by parts 59 Intuition behind Conditional Expectation 51 Probability of 3 people in a room of 30 having the same birthday 47 Probability for the length of the longest run in $n$ Bernoulli trials 41 Variance of sample variance?

### Reputation (28,373)

 +10 Finding the stationary distribution +10 Stirling's formula: proof? +10 Probability generating function of some “random walk” +10 Bounds for coefficients of bounded infinite series

### Questions (14)

 47 Convergence of $np(n)$ where $p(n)=\sum_{j=\lceil n/2\rceil}^{n-1} {p(j)\over j}$ 42 Rational solutions to $a+b+c=abc=6$ 38 Inequality for expected value 29 How to prove that $\int_0^1\left(\sum\limits_{k=n}^\infty {x^k\over k}\right)^2\,dx = \int_0^1 2x^{n-1}\log\left(1+{1\over\sqrt{x}}\right)\,dx$ 29 Does $2x^2-1=y^5$ have a solution in integers, with $y>1$?

### Tags (198)

 1k probability × 294 249 real-analysis × 70 446 probability-theory × 168 188 inequality × 35 302 combinatorics × 79 172 markov-chains × 98 286 stochastic-processes × 113 136 sequences-and-series × 34 279 measure-theory × 105 124 probability-distributions × 48

### Accounts (12)

 Mathematics 28,373 rep 358131 MathOverflow 2,262 rep 1222 Travel 610 rep 310 English Language & Usage 240 rep 18 Board & Card Games 171 rep 3