I know that Normal Distribution and Gaussian Distribution are the same thing, but today in class my teacher said that the mean of Gaussian Distribution = 0. I know that this isn't consistent with normal distributions, but rather standard normal distributions. Is the gaussian distribution the same as a normal distribution or a standard normal distribution, or am I wrong in thinking that the mean of every normal distribution can't be 0?
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5$\begingroup$ "normal distribution" = "Gaussian distribution." You can add the word "standard" to the beginning of both phrases to mean the specific distribution with mean 0 and variance 1. Your teacher probably meant to say standard Gaussian, but forgot or assumed you would understand. You are right that a normal distribution might not have mean zero. $\endgroup$– angryavianDec 14, 2017 at 22:32
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$\begingroup$ Normal $\equiv$ Gaussian. 'Standard normal' means $Norm(\mu=0, \sigma=1).$ Maybe your teacher was referring to a particular Gaussian (normal) distribution in the lecture. [I'm agreeing with @angryavian, but using slightly different words.] $\endgroup$– BruceETDec 15, 2017 at 4:19
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The teacher must have been speaking informally and relying on context to make it clear that a particular Gaussian distribution was his topic.
"Normal" and "Gaussian" in this context are synonymous.
The normal distribution was (probably) first introduced by Abraham de Moivre, who died before Gauss was born. De Moivre discovered an important special case of the central limit theorem. Gauss showed that only the normal distribution makes maximum likelihood coincide with least squares in certain problems.
