Figure 24 the variance of a bernoulli random variable

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Unformatted text preview: efinitions for independence of two or three events. Definition 2.4.7 Events A1 , A2 , . . . , An are independent if P (Ai1 Ai2 · · · Aik ) = P (Ai1 )P (Ai2 ) · · · P (Aik ) whenever 2 ≤ k ≤ n and 1 ≤ i1 < i2 < · · · < ik ≤ n. The definition of independence is strong enough that if new events are made by set operations on nonoverlapping subsets of the original events, then the new events are also independent. That is, suppose A1 , A2 , . . . , An are independent events, suppose n = n1 + · · · + nk with ni ≥ 1 for each i, and suppose B1 is defined by Boolean operations (intersections, complements, and unions) of the first n1 events E1 , . . . , En1 , B2 is defined by Boolean operations on the next n2 events, An1 +1 , . . . , An1 +n2 , and so on, then B1 , . . . , Bk are independent. 2.4. INDEPENDENCE AND THE BINOMIAL DISTRIBUTION 2.4.2 33 Independent random variables (of discrete-type) Definition 2.4.8 Discrete type random variables X and Y are independent if any event of the form X ∈ A is independent of any event...
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This note was uploaded on 02/09/2014 for the course ISYE 2027 taught by Professor Zahrn during the Spring '08 term at Georgia Tech.

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