LectureSept8

LectureSept8 - BME 423 Lecture Notes Sept 8 2008 Some Basic...

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Some Basic Probability Discrete Random Variables • Expected Value (Examples) Continuous Random Variables • Probability Density Function (pdf) • Cumulative Distribution Function (df) • Expected Value Using Standard Normal df Table BME 423 Lecture Notes - Sept. 8, 2008
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Discrete Probability Mass (Density) Function f(x) = Prob(X=x) x f(x) 12345 k x xxxx x 12 () , , , 0 e l s e w h e r e ik f xx x x fx = Properties 0 i 1 1 k i i = =
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Expected (or Mean) Value [] ( ) xD E Xx f x μ == x f(x) 1 2 1/2 Example () ( ) 11 12 1 . 5 22 EX x f x = =+ = Others Let X denote a discrete RV with values in set D and pdf f(x)
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Expected Value of a Function of X Let X denote a discrete RV with values in set D and pdf f(x) ( ) ( ) ( ) [] xD E hX hx f x = Define a function of X as h(x) x f(x) 1 2 1/2 Example ( ) () [] () 2 2 2 2.5 1.5 0.25 X X EX X == =− =
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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(50 75) HR < Probability Density Function (Continuous RV) Properties () 0 fx 1 f xdx −∞ = Probability density function ( pdf ):
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1. Uniform Density
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LectureSept8 - BME 423 Lecture Notes Sept 8 2008 Some Basic...

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