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Lecture3 - Random Variables Lecture 3 Random Variables and...

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1 Lecture 3 Random Variables and their Statistics Random Variables Recall we wanted an algebraic structure to combine various possible events from the sample space σ− field . To use the computational engine of calculus and set up a deductive ( conclude and predict) framework We map events from sample space to \ Definition of sets on How should sets and subsets be represented To accommodate unions and intersections? A function of one argument can be defined? Representation of subsets of by : Ex1: Suppose we want to represent a set with sets. \ \ ( , ] x −∞ ( , ] a b ( , ] x −∞ Continued Ex2: Ex3: ( , ] a b ( , ] ( , ] b a = −∞ − −∞ ( , ] ( , ] c b a = −∞ −∞ 1 1 { } lim{( , )} n a a a n n →∞ = + [ , ] ( , ] { } a b a b a = 1 1 { ( , ] ( , ] {lim ( , ]} c n b a a a n n → ∞ = − ∞ − ∞ +
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