49,862 reputation
463136
bio website linkedin.com/pub/…
location Illinois
age 39
visits member for 3 years, 7 months
seen 9 hours 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


18h
comment Are the poll results likely to be valid if they are based on only those subjects who agree to respond?
This question might be better suited for stats.stackexchange.com
Dec
17
comment Expectation of the maximum of gaussian random variables
An example, illustrating second point can be found here.
Dec
15
comment Calculating the Fourier transform of $\frac{\sinh(kx)}{\sinh(x)}$
@JohnZHANG It is obtained by writing sine as a linear combination of exponents, summing two geometric series and simplifying the result.
Dec
14
comment An intuitive understanding of the equation $Var(X)=E(X^2)-E(X)^2$
Is this a yes-or-no question? If so, the answer is in affirmative.
Dec
14
revised An intuitive understanding of the equation $Var(X)=E(X^2)-E(X)^2$
edited body
Dec
14
comment If $E[X(t)X(s)]=t \land s $. Show that this process has independent increments
HINT: Find the joint distribution of $X_{t_1}-X_{t_2}$ and $X_{t_3} - X_{t_4}$ assuming that $(t_1, t_2)$ and $(t_3, t_4)$ are disjoint.
Dec
14
revised If $E[X(t)X(s)]=t \land s $. Show that this process has independent increments
added 31 characters in body
Dec
14
answered Prove that $a_n = 2^n$
Dec
13
comment Need help to find $\int_0^\infty \frac{e^{-x^2}\sin x^2}{\ln(1+x^2)}dx$
Numeric value of the integral is $\approx 0.11304727$, and $-\frac{\pi^2}{12} \approx -0.822467 $. Voting to close.
Dec
13
answered Probability and stuff
Dec
12
revised probablity that $\max(X,Y)> a \min(X,Y)$
added 129 characters in body
Dec
12
answered probablity that $\max(X,Y)> a \min(X,Y)$
Dec
12
revised probablity that $\max(X,Y)> a \min(X,Y)$
added 22 characters in body; edited title
Dec
10
answered sum and difference between two independent Poisson random variables
Dec
10
revised sum and difference between two independent Poisson random variables
added 26 characters in body
Dec
9
awarded  Caucus
Nov
29
answered Determine the Density Function of $(X_1/X_2)$
Nov
25
comment When does $\int_0^t dX_s = X_t-X_0$ hold for a stochastic process?
What is the definition of stochastic integral you are working with?
Nov
15
comment Prove that $\frac{d^n}{dx^n} (\sin^4 x + \cos^4 x) = 4^{n-1}\cos (4x + \frac{n\pi}{2})$
Use $$ \sin^4(x) + \cos^4(x) = \frac{3}{4} + \frac{1}{4} \cos(4 x)$$ and an easy $\frac{d^n}{d x^n} \cos(a x) = a^n \cos\left(a x + \frac{\pi n}{2} \right)$.
Nov
6
revised Prove that a certain sequence of partial sums (involving integrals) converge.
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