Sample Spaces, Random Variables
نویسنده
چکیده
1 Probabilities In talking about probabilities, the fundamental object is Ω, the sample space. Points (elements) in Ω are denoted (generically) by ω. We assign probabilities to subsets of Ω. Assume for the moment that Ω is finite or countably infinite. Thus Ω could be the space of all possible outcomes when a coin is tossed three times in a row or say, the set of positive integers. A probability P is then a function from the power set (the class of all possible subsets) of Ω, which we will denote by A, to the interval [0, 1] satisfying the following properties: • (i) P (Ω) = 1 . • (ii) P (φ) = 0 . • (ii) If {An} is a sequence of mutually disjoint subsets of Ω, then,
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