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Unit Normal Distribution (Gaussian Distribution)

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This is a unimodal distribution, the mode being x = ¥ì, with two points of inflection (each located at a distance ¥ò to either side of the mode).  
The averages of n observations tend to become normally distributed as n increases. The variate x is said to be normally distributed if its density function f (x) is given by an expression of the form

f(x) = 1/(¥ò*(2*¥ð)^(1/2)) * e^(-(x-¥ì)/(2*¥ò^2))
¥ì = the population mean,
¥ò = the standard deviation of the population, and
-?¡Ä ¡Â x ¡Â ¡Ä
When ¥ì = 0 and ¥ò2 = ¥ò = 1, the distribution is called a standardized or unit normal distribution. Then

f(x) = 1/(2*¥ð)^(1/2) * e^(-(x^2)/2), where -?¡Ä ¡Â x ¡Â ¡Ä.


*** Âü°í¹®Çå[References] ***

NCEES, FUNDAMENTALS OF ENGINEERING SUPPLIED-REFERENCE HANDBOOK, 4th edition
f(x) = 1/(2*¥ð)^(1/2) * e^(-(x^2)/2)
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