Transcription of Sample Spaces, Random Variables - Statistics
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Sample Spaces, Random Variables - Statistics
Sample Spaces, Random VariablesMoulinath BanerjeeUniversity of MichiganAugust 30, 20121 ProbabilitiesIn talking about probabilities, the fundamental object is , the Sample space . Points(elements) in are denoted (generically) by .We assign probabilities to subsets of .Assume for the moment that is finite or countably infinite. Thus could be the spaceof all possible outcomes when a coin is tossed three times in a row or say, the set of probabilityPis then a function from the power set (the class of all possible subsets)of , which we will denote byA, to the interval [0,1] satisfying the following properties: (i)P( ) = 1.
The random variable Xis called a Bernoulli random variable. Example 2: This is also a discrete random variable that is composed by adding independent Bernoulli random variables.
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