Reputation
39,947
Next tag badge:
884/400 score
68/80 answers
Badges
3 86 147
Newest
 Nice Answer
Impact
~249k people reached

1d
awarded  Nice Answer
2d
revised Average distance between two randomly chosen points in unit square (without calculus)
added 808 characters in body
2d
answered Average distance between two randomly chosen points in unit square (without calculus)
2d
revised Independence of Random Variables
LaTeXify
2d
comment Independence of Random Variables
Hint. Notice that the $\sigma$-algebras satisfy $\sigma(f(X)) \subseteq \sigma(X)$ and $\sigma(g(Y)) \subseteq \sigma(Y)$. Also, what is the complement of a random variable?
May
21
revised prove that $f(z)+f(iz)=0$ please
added 538 characters in body
May
21
answered prove that $f(z)+f(iz)=0$ please
May
16
answered If $f:[0,1]\to\mathbf{R}$ is continuous, and that $\int_0^1 f(x)x^k \, dx = 0$ for all integers $k>2004$, show that $f = 0$.
May
16
comment If $f:[0,1]\to\mathbf{R}$ is continuous, and that $\int_0^1 f(x)x^k \, dx = 0$ for all integers $k>2004$, show that $f = 0$.
How about showing that $\tilde{f}(x) = x^{2005}f(x)$ is zero?
May
16
comment Integral of $\int_{-\infty}^\infty\frac{e^{-y^2/2} \sinh(cy)^2} {\cosh(Mcy) }dy$
@Boby, That's right. It is change of variable. Also, $\sec$ is correct. For example, the integral diverges to $\infty$ as $M \to 2^+$, and this phenomenon is exactly replicated by the answer.
May
15
answered Integral of $\int_{-\infty}^\infty\frac{e^{-y^2/2} \sinh(cy)^2} {\cosh(Mcy) }dy$
May
14
comment How to simplify this summation, or express as integral? $\sum_{t=-\infty}^\infty\frac1{\sqrt{(t+ax)^2+4}}$
Of course, you can always write it as $+\infty$.
May
13
awarded  Nice Answer
May
12
awarded  Good Answer
May
7
comment What is the difference between weak and strong law of large numbers?
My guess is that (1) SLLN is much harder to prove than WLLN (particularly in preliminary probability courses), and (2) they generalize in a slightly different way. Indeed, there exists an i.i.d. sequence $(X_n)$ of random variables for which WLLN holds but SLLN does not hold.
May
7
comment Is there a name for the relation $\int^b_a f(x)\ dx=\int_a^c f(x)\ dx+\int_c^b f(x)\ dx$?
I would call it additivity, since it generalizes to the additivity of the signed measure $E \mapsto \int_E f(x) \, dx$ with integrable $f$ (though this covers only the case $a\leq c\leq b$). But many preliminary analysis textbooks just seem to leave it unnamed.
May
6
awarded  Necromancer
May
4
awarded  Good Answer
May
4
comment On the inequality $ \int_{-\infty}^{+\infty}\frac{(p'(x))^2}{(p'(x))^2+(p(x))^2}\,dx \le n^{3/2}\pi.$
@DavidSpeyer, Thank you for the choosing my answer!
May
4
revised Computing $\int_{0}^{\infty} \frac{x^2 + a}{x^6 + a^3}dx$
added 2 characters in body