LEC_EAS305_F11_0919

# LEC_EAS305_F11_0919 - Random Variables Fall 2011 EAS 305...

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Random Variables Fall 2011 EAS 305 Lecture Notes Prof. Jun Zhuang University at Buﬀalo, State University of New York September 19, . .. 2011 Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 1 of 16

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Random Variables Agenda for Today 1 Random Variables Discrete Random Variables Continuous Random Variables Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 2 of 16
Random Variables Discrete Random Variables Continuous Random Variables Deﬁnition of Random Variable Deﬁnition: A random variable (RV) is a function from the sample space to the real line. X : S → < . Example: Flip 2 coins. S = { HH , HT , TH , TT } . Suppose X is the RV corresponding to the # of H ’s. X ( TT ) = 0, X ( HT ) = X ( TH ) = 1, X ( HH ) = 2. Pr( X = 0) = 1 4 , Pr( X = 1) = 1 2 , Pr( X = 2) = 1 4 . Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 3 of 16

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Random Variables Discrete Random Variables Continuous Random Variables Notation Notation: Capital letters like X , Y , Z , U , V , W usually represent RV’s. Small letters like x , y , z , u , v , w usually represent particular values of the RV’s. Thus, you can speak of Pr( X = x ). Prof. Jun Zhuang Fall 2011 EAS 305 Lecture Notes Page 4 of 16
Random Variables Discrete Random Variables Continuous Random Variables Example Example: Let X be the sum of two dice rolls. Then X ((4 , 6)) = 10. In addition, Pr( X = x ) = 1

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LEC_EAS305_F11_0919 - Random Variables Fall 2011 EAS 305...

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