9CommonDensities - Click to edit Master subtitle style EE...

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Unformatted text preview: Click to edit Master subtitle style EE 3180 Probability and Some Common Densities Jeffrey B. Burl EE 3180 Probability and 11 EE 3180 Probability and Normal/Gaussian Density n The normal or Gaussian density is: n where is the mean and σ2 is the variance. n The Gaussian density function (and therefore all probabilities) are fully specified by the mean and the variance! EE 3180 Probability and 22 2 1 2 1 ( ) 2 x X x f x e σ πσ-- = X 2 1 2 1 ( ) 2 u X x x F x e du σ πσ--- = 2 ( , ) N X σ EE 3180 Probability and Normal or Gaussian Density EE 3180 Probability and 33-2 2 4 6 8 10 0.05 0.1 0.15 0.2 x f x ( x )-2 2 4 6 8 10 0.5 1 x F x ( x ) EE 3180 Probability and Normal RVs Continued n The integral for generating the distribution function has no closed form solutions (same integral for computing probabilities for Normal RVs)! n Results tabulated or numerical solutions given in calculator, Matlab, Mathcad, etc. n Distribution function results usually given EE 3180 Probability and 44 EE 3180 Probability and Standard Normal RVs n The distribution function for the standard normal RV is often tabulated: n The distribution for other normal RVs is: n Note: EE 3180 Probability and 55 2 1 2 1 ( ) 2 x u x e du π-- Φ = ( ) x x X F x σ- = Φ ( 29 ( 29 1 x x Φ - = - Φ EE 3180 Probability and Standard Normal RVs, Continued n The Q function is related to standard normal RVs and often tabulated: n The distribution for other normal RVs is:...
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This note was uploaded on 06/16/2010 for the course EE ee3180 taught by Professor Burl during the Spring '10 term at Michigan Technological University.

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9CommonDensities - Click to edit Master subtitle style EE...

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