LectureSept2-2

# LectureSept2-2 - BME 423 Lecture Notes Sept 2 2009(updated...

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1 Some Basic Probability Discrete Random Variables • Expected Value (Example) Continuous Random Variables • Probability Density Function (pdf) • Cumulative Distribution Function (df) • Expected Value Using Standard Normal df Table BME 423 Lecture Notes - Sept. 2, 2009 (updated 9/2/2009) Discrete Probability Function (pf) f(x) = Prob(X=x) x f(x) 12345 k xxxxx x 12 () , , , () 0 e l s ew h e r e ik f xx x x fx = () 0 i Properties 1 ()1 k i i = =

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2 Expected Value of a Function of X Let X denote a discrete RV with values in set D and pf f(x) () ( ) ( ) [] xD EhX hx f x = x f(x) 1 2 1/2 Examples ( ) ( ) 11 ( )1 2 22 1.5 EX x f x == + = x f(x) 1 2 1/2 Examples ( ) ( ) () [] () () 2 2 2 2 2 ( ) 1 2 2.5 1.5 1.5 ( ) ( 0.5) (0.5) 0.25 hX X xfx X EX E X EX E X xf x ⎡⎤ = + = ⎣⎦ =− = + = ( ) 2 X = ( ) 2 ( ) Eh X Find: Variance of X
3 How to describe the “degree of randomness” of a continuous RV X? () f x Prob( ) ( ) b a aXb f x d x <≤= f ( x ) 100 200 0 x HR (beats/min) Prob(75 100) HR < Probability Density Function (Continuous RV) Properties () 0 fx 1 f xdx −∞ = Probability density function (pdf): 1. Uniform pdf (Uniform Density)

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## This note was uploaded on 10/13/2009 for the course BME 423 at USC.

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LectureSept2-2 - BME 423 Lecture Notes Sept 2 2009(updated...

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