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Chapter 4 RANDOM VARIABLES

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 r

DEFINITION: A random variable is said to be continuous if its cdf is a continuous function (see later). This is an important case, which occurs frequently in practice. EXAMPLE: The Exponential Distribution Consider the rv Y with cdf FY (y) = 0, y < 0, 1 − e−y, y ≥ 0. This meets all the requirements above, and is not a step function.

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