Question

What is the purpose of $\frac{1}{\sigma \sqrt{2 \pi}}$ in $\frac{1}{\sigma \sqrt{2 \pi}}e^{\frac{(-(x - \mu ))^2}{2\sigma ^2}}$?

score 17.5k · Answer 1 · 2026-03-25 12:50:03

17.5k

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What is the purpose of $\frac{1}{\sigma \sqrt{2 \pi}}$ in $\frac{1}{\sigma \sqrt{2 \pi}}e^{\frac{(-(x - \mu ))^2}{2\sigma ^2}}$?

Published on 25 Mar 2026 - 12:50

score 114 · Answer 2 · 2019-04-10 18:02:13

114

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Can we define the Gaussian distribution by taking the power of 2 instead of the exponential function?

Published on 10 Apr 2019 - 18:02

score 1.3k · Answer 3 · 2019-04-10 18:25:41

1.3k

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sum of 3 correlated jointly random variables

Published on 10 Apr 2019 - 18:25

score 54 · Answer 4 · 2019-04-11 04:37:55

54

Views

$\int_{-\infty}^\infty \frac{1}{\sqrt{2\pi\sigma^2}} e^{(-1/2)((x-\mu)/\sigma)^2} dx = 1$, no polar coordinates

Published on 11 Apr 2019 - 4:37

score 357 · Answer 5 · 2026-03-26 01:11:45

357

Views

Derivation of expected value of $\exp(-aX^2)$ when $X$ is normally distributed

Published on 26 Mar 2026 - 1:11

score 858 · Answer 6 · 2019-04-11 08:38:26

858

Views

what is a standard complex gaussian random variable?

Published on 11 Apr 2019 - 8:38

score 39 · Answer 7 · 2026-03-28 14:54:17

39

Views

probability of event on two random variables and their sum

Published on 28 Mar 2026 - 14:54

score 32 · Answer 8 · 2019-04-11 16:07:21

32

Views

A die roll and Binomial distribution.

Published on 11 Apr 2019 - 16:07

score 60 · Answer 9 · 2019-04-11 20:28:20

60

Views

Is it always true if two random variables are jointly Gaussian, then they must be individually Gaussian as well?

Published on 11 Apr 2019 - 20:28

score 69 · Answer 10 · 2026-03-25 04:35:44

69

Views

Compute component probabilities in EM-algorithm with log densities?

Published on 25 Mar 2026 - 4:35

score 68 · Answer 11 · 2026-03-25 23:10:37

68

Views

Distribution/Variance of correlated squared normal random variables

Published on 25 Mar 2026 - 23:10

score 141 · Answer 12 · 2026-03-26 06:22:32

141

Views

Find the best unbiased estimator for $\mu^T \mu + 1^T \mu$.

Published on 26 Mar 2026 - 6:22

score 29 · Answer 13 · 2019-04-14 17:26:35

29

Views

On probability and standard deviation

Published on 14 Apr 2019 - 17:26

score 92 · Answer 14 · 2026-03-29 21:52:53

92

Views

Conditional expectation for multivariate normal distribution

Published on 29 Mar 2026 - 21:52

score 31 · Answer 15 · 2026-03-25 23:15:58

31

Views

Identify which normal distribution generated a given sample

Published on 25 Mar 2026 - 23:15

List Question

What is the purpose of $\frac{1}{\sigma \sqrt{2 \pi}}$ in $\frac{1}{\sigma \sqrt{2 \pi}}e^{\frac{(-(x - \mu ))^2}{2\sigma ^2}}$?

Can we define the Gaussian distribution by taking the power of 2 instead of the exponential function?

sum of 3 correlated jointly random variables

$\int_{-\infty}^\infty \frac{1}{\sqrt{2\pi\sigma^2}} e^{(-1/2)((x-\mu)/\sigma)^2} dx = 1$, no polar coordinates

Derivation of expected value of $\exp(-aX^2)$ when $X$ is normally distributed

what is a standard complex gaussian random variable?

probability of event on two random variables and their sum

A die roll and Binomial distribution.

Is it always true if two random variables are jointly Gaussian, then they must be individually Gaussian as well?

Compute component probabilities in EM-algorithm with log densities?

Distribution/Variance of correlated squared normal random variables

Find the best unbiased estimator for $\mu^T \mu + 1^T \mu$.

On probability and standard deviation

Conditional expectation for multivariate normal distribution

Identify which normal distribution generated a given sample

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