Normal Distribution

Tags

PAS

Cegep/2

Word count

95 words

Reading time

1 minute

Absolutely continuous probability distribution
Sym. $N(\mu ,{\sigma }^2)$
Syn. Gaussian distribution

[!abstract] Bell curve
Curve of a normal distribution

[!abstract] Standard normal distribution
Normal distribution with $\mu =0$ and $\sigma =1$
Sym. $Z$

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Properties

$$P(X=k)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{-\frac{1}{2}{\left(\frac{k-\mu }{\sigma }\right)}^2},-\mathrm{\infty }<k<\mathrm{\infty }$$

• Linear transformations of normal variables are normal variables.
• Sums / differences of independent normal variables are normal variables.

$$X,Y\sim N⟹(aX+b),(X\pm Y)\sim N$$

Contributors

Ajitani Hifumi

Changelog

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