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L12posted - Continuous Random Variables Continuous random...

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Unformatted text preview: Continuous Random Variables Continuous random variables are random variables that arise from measurements can take any value in interval Example .Random numbers in [0 , 1] used in random number genera- tors. 1 . Think of a circle with circumfer- ence 1 and a pointer attached in the center. Give it a long spin. Points to a random direction. 0.5 0.75 0.25 X =location of the pointer. Note . For any point a, we have P ( X = a ) = 0 2 . Described by a probability density function f ( x ) f ( x ) < Total area under the graph is 1 Z + - f ( x ) dx = 1 Interpretation. P ( a < X b ) = R b a f ( x ) dx Graphical Meaning. 3 Uniform f ( x ) = 1 b- a , if a < x < b , otherwise 4 Triangular 5 Exponential f ( x ) = 1 e- x if x otherwise 6 Loss of Memory Property of Ex- ponential . Let X be exponential and a,b > P ( X > b + a | X > a ) = P ( X > b + a,X > a ) P ( X > a ) = P ( X > b + a ) P ( X > a ) = e-- ( b + a ) e- a = e- a = P ( X > b ) 7 Normal (also called Gaussian) f ( x ) = 1 2 e- 1 2 x- 2 8 Expected Value...
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This note was uploaded on 01/03/2012 for the course EE 1244 taught by Professor Drera during the Fall '10 term at Conestoga.

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L12posted - Continuous Random Variables Continuous random...

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