6DensityFunctions

# 6DensityFunctions - The Probability Density Function...

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Click to edit Master subtitle style  EE 3180 Probability and  The Probability Density  Function Jeffrey B. Burl 11

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EE 3180 Probability and  The Density Function n The probability density function (PDF) is more  convenient than the distribution function for  many calculations. n The density function is the derivative of the  distribution function: 22 ( ) ( ) x x dF x f x dx =
EE 3180 Probability and  Interpretation of the Density  Function n The density function can be interpreted: n Probabilities can be computed from the  density function: n The analogy with density and mass is good. 33 ( ) Pr( ) x f x dx x X x dx = < + 2 1 1 2 Pr( ) ( ) x x x x X x f x dx < =

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EE 3180 Probability and  Density Function Properties n The density function has the following  properties: 44 ( ) 0 for all x f x x - < < ( ) 1 x f x dx d - = ( ) ( ) x x x F x f x dx - =
EE 3180 Probability and  Example 1 n Flip a coin.

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6DensityFunctions - The Probability Density Function...

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