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Jan
27
comment What does “variance unity” mean?: “A normal distribution with mean $\mu$ and variance unity”.
Often the correct way to say it is "unit variance".
Jan
22
comment Doob-style second moment martingale inequality
You might be interested in the Cantelli Inequality
Dec
30
accepted Weak Law of large numbers involving a sequence and random variable
Dec
30
comment Weak Law of large numbers involving a sequence and random variable
Thanks for the elegant solution Davide... It's good to know that it held in strong sense as well.
Dec
29
revised Prove that $\sqrt{x_1}+\sqrt{x_2}+\cdots+\sqrt{x_n} \geq (n-1) \left (\frac{1}{\sqrt{x_1}}+\frac{1}{\sqrt{x_2}}+\cdots+\frac{1}{\sqrt{x_n}} \right )$
Corrected the condition term
Dec
28
revised Weak Law of large numbers involving a sequence and random variable
added 299 characters in body
Dec
28
revised Weak Law of large numbers involving a sequence and random variable
added 1228 characters in body
Dec
27
asked Weak Law of large numbers involving a sequence and random variable
Dec
16
comment product of two uniformly continuous functions is uniformly continuous
Have you checked this site for a solution? If you don't find the solution, try posting this question giving your workouts etc.
Dec
16
comment product of two uniformly continuous functions is uniformly continuous
On $[0,1]$, let $f(x)=1$ if $x$ is rational and $-1$ otherwise. Then $f$ is not continuous (let alone uniformly), but $f^2$ is constant!!
Dec
13
comment Proving $\lim_{n \to \infty} \frac {\log{p_n}} {\log n} = 1$
Could you tell us your background. Along with where you encountered this question?
Dec
11
revised cardinality of the set of points with one irrational coordinate, and one rational.
Edited the title. carnality -> cardinality
Dec
10
comment Prove that $\sigma^2_{X+Y}=\sigma_X^2+\sigma_Y^2$ without independence
I'm not clear when you say "without using independence".
Dec
10
comment Prove that $\sigma^2_{X+Y}=\sigma_X^2+\sigma_Y^2$ without independence
This is the part where you use $f_{XY}(x,y) = f_X(x)f_Y(y)$ as $X$ and $Y$ are independent.
Dec
9
comment All derivatives zero at a point $\implies$ constant function?
Oh. I misread some $a \in \mathbb{R}$ for all $a \in \mathbb{R}$. Kindly ignore my hint.
Dec
5
answered How to expand $|(1-H(f))|^2$, $H(f)$ is complex.
Nov
29
awarded  Nice Answer
Nov
25
accepted Compactness of Set of Probability Measures
Nov
25
comment Compactness of Set of Probability Measures
This is also a very good and simple proof... probably simpler than mine. Thanks.
Nov
21
answered Compactness of Set of Probability Measures