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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.(a)Construct a table that shows the values of the ran-dom variableXfor each possible outcome of therandom experiment.(b)Identify the event{X 1}in the difference between the number of headsobtained and the number of tails obtained.

RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS 3.1 Concept of a Random Variable Random Variable A random variable is a function that associates a real number with each element in the sample space. In other words, a random variable is a function X :S!R,whereS is the sample space of the random experiment under consideration. N OTE.

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