Lecture 3 : Probability Theory - MIT OpenCourseWare

Lecture 3 : Probability and reviewWe consider real-valued discrete random variables and continuous ran-dom variables. A discrete random variableXis given by itsprobabilitymass function which is a non-negative real valued functionfX: R 0satisfyingx fX(x) = 1 for some finite domain known as thesample space. For example,2/3 (x=1)fX(x) = 1/3 (x= 1),0(otherwise)denotes the Probability mass function of a discrete random variableXwhichtakes value 1 with Probability 2/ 3 and 1 with Probability 1 continuous random variableYis given by itsprobability density func-tionwhich is a non-negative real valued functionfY: R 0satisfying fY(y)dy=1 (we will mostly consider cases when the sample space is the realsR). For example,1 (y[0,1])fY(y) ={ ,0 (otherwise)denotes the Probability density function of a continuous random variableYwhich takes a uniform value in the interval [0,1].}

Lecture 3 : Probability Theory 1. Terminology and review We consider real-valued discrete random variables and continuous ran-dom variables. A discrete random variable X is given by its probability mass functionP which is a non-negative real valued function f …

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