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	Probability density function; The red line is the standard normal distribution
	Cumulative distribution function; Colors match the image above
Notation
Parameters	μ ∈ R — mean (location); σ2 > 0 — variance (squared scale)
Support	x ∈ R
PDF
CDF
Mean	μ
Median	μ
Mode	μ
Variance	σ2
Skewness	0
Excess kurtosis	0
Entropy
MGF
CF
Fisher information

Notation

{\mathcal {N}}(\mu ,\,\sigma ^{2})

Parameters μ ∈ R — mean (location)
σ² > 0 — variance (squared scale)

Support x ∈ R

{\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}

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Probability density function The red line is the standard normal distribution
Cumulative distribution function Colors match the image above
Notation	${\mathcal {N}}(\mu ,\,\sigma ^{2})$
Parameters	μ ∈ R — mean (location) σ² > 0 — variance (squared scale)
Support	x ∈ R
PDF	${\frac {1}{\sqrt {2\pi \sigma ^{2}}}}\,e^{-{\frac {(x-\mu )^{2}}{2\sigma ^{2}}}}$
CDF	${\frac {1}{2}}\left[1+\operatorname {erf} \left({\frac {x-\mu }{\sqrt {2\sigma ^{2}}}}\right)\right]$
Mean	μ
Median	μ
Mode	μ
Variance	σ²
Skewness	0
Excess kurtosis	0
Entropy	${\frac {1}{2}}\ln(2\pi e\,\sigma ^{2})$
MGF	$\exp\{\mu t+{\frac {1}{2}}\sigma ^{2}t^{2}\}$
CF	$\exp\{i\mu t-{\frac {1}{2}}\sigma ^{2}t^{2}\}$
Fisher information	${\begin{pmatrix}1/\sigma ^{2}&0\\0&1/(2\sigma ^{4})\end{pmatrix}}$

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