LectureSept10

LectureSept10 - BME 423 Lecture Notes - Sept. 10, 2008 Some...

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Some Basic Probability Summary Discrete RV Summary Continuous RV Using Standard Normal cdf Table BME 423 Lecture Notes - Sept. 10, 2008
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Probability Mass Function f(x) = Prob(X=x)=P(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 = ( ) : () P r o b ( ) yy x Fx X x fy =≤ = Cumulative Distribution Function (cdf) x f(x) k x Discrete Random Variable X
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Expected Value [] ( ) xD E Xx f x μ == Let X denote a discrete RV with values in set D and pdf f(x) ( ) ( ) ( ) E hX hx f x = Define a function of X as h(x)
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Probability Density Function Cumulative Distribution Function (cdf) Continuous Random Variable X Prob( ) ( ) b a aXb f x d x <≤ = f ( x ) 0 x 0 ab () Fx x fxd x −∞ = P ( ) F xX x =< x
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Expected Value Let X denote a continuous RV with Define a function of X as g(x) ~( ) X fx [] ( ) EX x f xdx μ −∞ = [ () ] Egx gx f xdx −∞ =
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Let X denote the amount of time for which a book on 2 hour reserve is check out by a random student. Assume the pdf for X is () 0 . 5 0 2 0o t h e r w i s e fx x x =≤ = a)
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LectureSept10 - BME 423 Lecture Notes - Sept. 10, 2008 Some...

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