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# Lecturenotes10 - STAT 430/510 Lecture 10 STAT 430/510...

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STAT 430/510 Lecture 10 STAT 430/510 Probability Hui Nie Lecture 10 June 15th, 2009

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STAT 430/510 Lecture 10 Introduction The set of possible values for discrete random variable is either ﬁnite or countably inﬁnite However, there also exist random variables whose set of possible values is uncountable.
STAT 430/510 Lecture 10 Deﬁnition of Continuous Random Variable X is a continuous random variable if there exists a nonnegative function f , deﬁned for all real x ( -∞ , ) , having the property that, for any set B of real numbers P ( X B ) = Z B f ( x ) dx The function f is called the probability density function of random variable X . The cumulative probability function is given by F ( x ) = P ( X x ) = Z x -∞ f ( s ) ds

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STAT 430/510 Lecture 10 Properties of Continuous Random Variable 1 = P ( X ( -∞ , )) = R f ( x ) dx P ( a X b ) = R b a f ( x ) dx P ( X = a ) = R a a f ( x ) dx = 0 P ( X < a ) = P ( X a ) = R a f ( x ) dx
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Lecturenotes10 - STAT 430/510 Lecture 10 STAT 430/510...

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