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Unformatted text preview: function of the Normal distribution looks like a bell, which is
completely symmetrical and peaks in the center.
The density function has a positive “mass” on any value of x, which means the outcome of
this random event can be any value from −∞ to ∞.
The probability density function peaks in the center of this distribution, meaning the outcome of the random event is most likely to be this center value. This center position is the
mean, median and the mode of the Normal distribution.
The likelihood of the outcome being x dies down very fast from this center. The “tightness”
of the distribution is determined by the standard deviation (or variance) of the distribution.
Remark. Important Properties of the Normal Density Function
1.
2.
3.
4.
5. unimodal
symmetrical
mean = median = mode
approaches both −∞ and ∞ on the x axis (asymptotic to the x axis)
the spread is controlled by the variation Deﬁnition. The probability density functi...
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 Fall '13
 Alexandru
 Probability

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