48,597 reputation
462134
bio website linkedin.com/pub/…
location Illinois
age 39
visits member for 3 years, 4 months
seen 47 mins ago

I'm a mix of things, a physicist by education, I earn my living as a mathematician and programmer working at Wolfram Research. I thoroughly enjoy learning and discovery process.


“Technical skill is mastery of complexity, while creativity is mastery of simplicity”
— Erik Christopher Zeeman

Project Euler


16h
comment Probability that a company is worth $xM after y years, if its value can only stay the same or double every year?
you are on the right track...
1d
awarded  Nice Answer
Sep
19
awarded  improper-integrals
Sep
16
revised Limit of Lambert $W$ Product Log is the Natural Log?
added 29 characters in body
Sep
15
comment Other ways to evaluate $\lim_{x \to 0} \frac 1x \left [ \sqrt[3]{\frac{1 - \sqrt{1 - x}}{\sqrt{1 + x} - 1}} - 1\right ]$?
@rubik This is simply a consequence of $a^3 - b^3 = \left(a-b\right)\left(a^2+ a b + b^2\right)$ for $a=\sqrt[3]{1+w}$ and $b=1$.
Sep
15
answered Other ways to evaluate $\lim_{x \to 0} \frac 1x \left [ \sqrt[3]{\frac{1 - \sqrt{1 - x}}{\sqrt{1 + x} - 1}} - 1\right ]$?
Sep
6
revised Showing that $\mathbb{E}|X\ln X| < \infty$ and $\mathbb{E}Z = \mathbb{E} X \ln X$ for given PDF of $Z$.
added 124 characters in body
Sep
4
comment Showing that $\mathbb{E}|X\ln X| < \infty$ and $\mathbb{E}Z = \mathbb{E} X \ln X$ for given PDF of $Z$.
@Did My bad, the inequality should have been $\vert X \ln X \vert \leqslant \max\left(\mathrm{e}^{-1},X^2\right)$.
Aug
31
answered Probability You Choose at least one chip of every color
Aug
31
answered The density of conditional distribution.
Aug
31
revised The moment generating function of the geometric distribution
added 20 characters in body
Aug
31
answered Cramer-Rao lower bound always possible?
Aug
30
revised Question for recommending a good textbook in representation of quivers
added 83 characters in body; edited title
Aug
30
revised Showing that $\mathbb{E}|X\ln X| < \infty$ and $\mathbb{E}Z = \mathbb{E} X \ln X$ for given PDF of $Z$.
added 161 characters in body
Aug
30
answered Showing that $\mathbb{E}|X\ln X| < \infty$ and $\mathbb{E}Z = \mathbb{E} X \ln X$ for given PDF of $Z$.
Aug
28
comment A Markov Chain Problem.(Change the color of ball)
@tan9p Could you please cite the origin of the problem? Thank you. Also please see my answer to the related question 910601.
Aug
28
comment A Markov Chain Problem.(Change the color of ball)
+1 The exact expression is $\mathrm{E}\left(\tau\right) = 1 + \sum_{k=1}^{n-2} \frac{n(n-1)}{k(k+1)} = (n-1)^2$, since the sum telescopes. See problem 910601 for more detailed.
Aug
28
comment Probability: the average times to make all the balls the same color
@Peter Could you please cite the origin of the problem? Thank you.
Aug
28
revised Probability: the average times to make all the balls the same color
added 874 characters in body
Aug
28
comment Probability of order statistics with numerous conditions
Can one assume $Y$ to be a continuous random variable?