隨機變數
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它的 *pdf* 如下

The normal distribution with a mean of and a standard deviation of is denoted by .

Interpreting the parameters, we can see in follow that a change of mean from to a larger value merely slides the bell-shaped curve along the axis until a new center is established at . There is no change in the shape of the curve.

A different value for the standard deviation results in a different maximum height of the curve and changes the amount of the area in any fixed interval about as follow. The position of the center does not change if only is changed.