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Chapter 4 RANDOM VARIABLES - University of Kent

Chapter 4 RANDOMVARIABLESE xperiments whose outcomes arenumbersEXAMPLE:Selectitemsat randomfrom a batch of sizeNuntil the first defective item is number of non-defective Space:S={0,1,2,..,N}The result from the experiment becomes avariable; that is, a quantity taking differentvalues on different occasions. Because theexperiment involves selection at RANDOM , wecall it arandom : rvNotation: capital letter, :The set of possible values that a randomvariableXcan take is called RandomExperiment VariableEXSample space range ofXOutcome ofEOne possible valuexforXEventSubset of range ofXEventAx subset of range ,x= 3 or 2 x 4Pr(A)Pr(X= 3),Pr(2 X 4)REMINDER:The set of possible values that a randomvariable (rv)Xcan take is called :A rvXis said to bediscreteif its rangeconsists of afiniteorcountablenumber : based on tossing a coin repeatedlyNo.

behaviour of a (discrete) random variable. In practice we often want a more concise description of its behaviour. DEFINITION: The mean or expectation of a discrete rv X, E(X), is defined as E(X) = X x xPr(X = x). Note: Here (and later) the notation X x means the sum over all values x in the range of X. The expectation E(X) is a weighted ...

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