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r7_gaussian

# r7_gaussian - 13.42 Design Principles for Ocean Vehicles...

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13.42 Design Principles for Ocean Vehicles Prof. A.H. Techet Spring 2005 1. Gaussian Distribution Distributions of random variables are often gaussian in shape, or can be approximated as such. The gaussian density function is described by the probability density function 1 ( x x ) 2 ( ) = 2 e 2 σ 2 (1) f x 2 πσ which is symmetric about x . Given this pdf the cumulative probability of x is x x 1 + erf σ F x ( ) = (2) 2 where erf is the error function: 0 2 e / 2 dy ζ erf ( ) = 1 ζ y (3) 2 π For an approximately normal function (with Gaussian distribution) then 68% of events fall within 1 σ 95% of events fall within 2 σ 97.7% of events fall within
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