User Alecos Papadopoulos

68 votes

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Why the sum of residuals equals 0 when we do a sample regression by OLS?

answered Sep 17, 2013 at 21:40

49 votes

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how to derive the mean and variance of a Gaussian Random variable?

answered Oct 9, 2013 at 0:43

38 votes

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Identity for simple 1D random walk

answered Jan 8, 2014 at 21:38

30 votes

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Derivation of the density function of student t-distribution from this big integral.

answered Aug 31, 2013 at 1:10

15 votes

How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$

answered Dec 9, 2013 at 4:38

12 votes

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What is the difference between a random vector and a stochastic process?

answered Nov 17, 2013 at 23:49

12 votes

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Why would I use Bayes' Theorem if I can directly compute the posterior probability?

answered Aug 30, 2013 at 19:25

11 votes

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Why the expected value of the error when doing regression by OLS is 0?

answered Sep 18, 2013 at 1:29

10 votes

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Expectation Operator on a Matrix

answered Jan 20, 2014 at 1:36

10 votes

Is Standard Deviation the same as Entropy?

answered Jan 25, 2014 at 19:59

10 votes

Can the maximum likelihood estimator be unbiased and fail to achieve Cramer-Rao lower bound?

answered May 26, 2014 at 2:57

10 votes

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Is the mean of the truncated normal distribution monotone in $\mu$?

answered Jul 30, 2013 at 18:12

9 votes

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Conditional mean on uncorrelated stochastic variable

answered Jan 4, 2014 at 15:20

9 votes

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Teaser or fun calc equation to surprise husband (physicist/EE) at work

answered Sep 12, 2013 at 2:48

7 votes

Product of two complementary error functions (erfc)

answered Nov 1, 2013 at 0:38

7 votes

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Asymptotic correlation between sample mean and sample median

answered Sep 13, 2013 at 0:52

6 votes

Accepted

Moment generating function of a constant

answered Jan 13, 2016 at 13:13

6 votes

Process properties of the maximum of two independent linear Brownian motions

answered Jun 17, 2017 at 15:04

6 votes

Help me organize these concepts -- KKT conditions and dual problem

answered Sep 11, 2013 at 22:49

6 votes

Is it possible to alternate the law of mathematics?

answered Aug 28, 2013 at 19:04

5 votes

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Closed form solution to $\int_0^{\infty} x(1+({\frac{x}{\lambda}})^{(-\alpha-1)}) dx$

answered Sep 20, 2019 at 20:23

5 votes

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Correct Intuition? Standard Deviation and distance in $n$ dimensional space.

answered Sep 3, 2015 at 20:40

5 votes

Are we guaranteed that the harmonic series minus infinite random terms always converge?

answered Jun 15, 2016 at 2:55

5 votes

Is there a mathematical reason why chocolate chip cookies have 37% (1/e) chocolate in them?

answered Jan 26, 2014 at 11:43

5 votes

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Least squares / residual sum of squares in closed form

answered Apr 17, 2014 at 0:26

5 votes

Maximum Entropy (The existence of a Calculus of Variations problem)

answered Dec 11, 2013 at 18:36

5 votes

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Mapping CDF's to each other

answered Dec 10, 2013 at 17:05

5 votes

Relationship between entropy and ergodicity

answered Aug 4, 2013 at 11:37

4 votes

Clayton copula and Kendall's tau

answered Jan 15, 2014 at 2:09

4 votes

Accepted

geometric CDF converges to exponential cdf

answered Nov 15, 2014 at 20:53

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218 Answers

Why the sum of residuals equals 0 when we do a sample regression by OLS?

how to derive the mean and variance of a Gaussian Random variable?

Identity for simple 1D random walk

Derivation of the density function of student t-distribution from this big integral.

How to prove $\int_0^1\tan^{-1}\left[\frac{\tanh^{-1}x-\tan^{-1}x}{\pi+\tanh^{-1}x-\tan^{-1}x}\right]\frac{dx}{x}=\frac{\pi}{8}\ln\frac{\pi^2}{8}?$

What is the difference between a random vector and a stochastic process?

Why would I use Bayes' Theorem if I can directly compute the posterior probability?

Why the expected value of the error when doing regression by OLS is 0?

Expectation Operator on a Matrix

Is Standard Deviation the same as Entropy?

Can the maximum likelihood estimator be unbiased and fail to achieve Cramer-Rao lower bound?

Is the mean of the truncated normal distribution monotone in $\mu$?

Conditional mean on uncorrelated stochastic variable

Teaser or fun calc equation to surprise husband (physicist/EE) at work

Product of two complementary error functions (erfc)

Asymptotic correlation between sample mean and sample median

Moment generating function of a constant

Process properties of the maximum of two independent linear Brownian motions

Help me organize these concepts -- KKT conditions and dual problem

Is it possible to alternate the law of mathematics?

Closed form solution to $\int_0^{\infty} x(1+({\frac{x}{\lambda}})^{(-\alpha-1)}) dx$

Correct Intuition? Standard Deviation and distance in $n$ dimensional space.

Are we guaranteed that the harmonic series minus infinite random terms always converge?

Is there a mathematical reason why chocolate chip cookies have 37% (1/e) chocolate in them?

Least squares / residual sum of squares in closed form

Maximum Entropy (The existence of a Calculus of Variations problem)

Mapping CDF's to each other

Relationship between entropy and ergodicity

Clayton copula and Kendall's tau

geometric CDF converges to exponential cdf