Let X be random variable and X~N(u,σ^2)(adsbygoogle = window.adsbygoogle || []).push({});

Thus, normal distribution of x is

f(x) = (1/σ*sqrt(2π))(e^(-(x-u)^2)/(2σ^2)))

If we want to standardize x, we let z=(x-u)/σ

Then the normal distribution of z becomes

z(x) = (1/σ*sqrt(2π))(e^(-(x^2)/(2))

and we usually write Z~N(0,1)

But as you can see, sigma in z(x) does not disappear. Thus, in my opinion Z~N(0,1) should be actually written as Z~(1/σ)N(0,1). So here goes my question :

why does every textbook use the notation Z~N(0,1), not Z~(1/σ)N(0,1)

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# On standardization of normal distribution

Loading...

Similar Threads for standardization normal distribution |
---|

A Sample Test | Component Lifetime |

I Understanding the transformation of skewness formula |

I Standard Deviation Versus Sample Size & T-Distribution |

I Standard deviation of data after data treatment |

**Physics Forums | Science Articles, Homework Help, Discussion**