M4L14 - M4L1 Functions of Single Random Variables 1...

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    M4L1 Functions of Single Random Variables 1. Introduction This is the first lecture on functions of Random Variables . Different functions of Random Variable along with their properties are discussed. Determination of pdf and CDF of those functions are also discussed. 2. Functions of Random Variable As discussed in Module 3, Random Variable (RV) is a function that maps the outcomes of an experiment over a sample space to a numerical value on the real line. Any function of , say , is also a Random Variable, denoted as . Formally this function is defined as, a function of single random variable, , which is a composite function of with domain set of experimental outcomes (Papoulis and Pillai, 2002). For an outcome is a number and as another number specified in terms of and  X g . Now the function of a random variable at can be represented as and value of this number can be taken as: as assigned to Random Variable, Y. Thus a function of random variable is a composite function with domain set, S of experimental outcomes. The CDF of , for the Random Variable (function of ), defines the probability of the event consists of all outcomes,
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M4L14 - M4L1 Functions of Single Random Variables 1...

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