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.(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.
Continuous Random Variable If a sample space contains an infinite number of pos-sibilities equal to the number of points on a line seg-ment, it is called a continuous sample space. When a random variable can take on values on a continuous scale, it is called a continuous random variable. E XAMPLE 3.5. Categorize the random variables in the
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