Continuous Random Variables and PMFs, Lecture notes of Probability and Stochastic Processes

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S-\. Contin uous andor. Narrables ard PMFs Random yariable X is called covtinuouS WF there o_| [nan- negatne Function calle ch f) 5 collad the Probability density Funckton of XK ss P(x é€ = Je x) dx b Pleexeb) = Spb) ax Norwni lization propsrty : S f Gel due Pl- cot x4eo0)=! rote Fe) zo fee every value of ye for A Very a; avers d, P(Cx, xt dD) ee Uae = FG. é Unk wnt, Distibuted Por VA T. (x)* { ti] letl alexle b b-a fo) otherwise Expectation “Tre expected value or expectation or mean of a _continnous random veriable & is defined by E [xJ- fr xF OD dx ELscw) aie qet.o dx ver Go~ E [(x- ELy J » Se ) ac) dx oz ye toe ER T-(EDIY