Transcription of 3.1 Concept of a Random Variable
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3.1 Concept of a Random Variable
CHAPTER3 Random VARIABLES AND PROBABILITY Concept of a Random VariableRandom VariableArandom variableis a function that associates a realnumber with each element in the sample other words, a Random Variable is a functionX:S!R,whereSis the sample space of the randomexperiment under convention, we use a capital letter, sayX,to denote a Random Variable , and use the correspondinglower-case letterxto denote the realization (values) ofthe Random (Coin).Consider the Random experi-ment of tossing a coin three times and observing the re-sult (a Head or a Tail) for each toss. LetXdenote thetotal number of heads obtained in the three tosses of thecoin.
T is a random variable. Discrete Random Variable If a sample space contains a finite number of possibil-ities or an unending sequence with as many elements as there are whole numbers (countable), it is called a discrete sample space. A random variable is called a discrete random variable if its set of possible outcomes is countable.
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