ISEN 609 Lecture 7

# ISEN 609 Lecture 7 - 7 Sequences of Random Variables Most dynamic phenomena are modeled using collections of random variables(measurements over

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7. Sequences of Random Variables Most dynamic phenomena are modeled using collections of random variables (measurements over time): waiting lines sequential decision processes reliability and maintenance project management etc. We will use the concepts we have learned to study sequences of random variables

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Simplest Case: Independent Sequences Random sample -- an independent, identically distributed ( i.i.d. ) sequences of random variables This sequence is completely described by a single distribution function F Because of independence, we can figure the probability of any event related to this sequence by “decomposing” the joint probability into a product of marginal probabilities X 1 , X 2 , . . . , X n , . . .
Limit Theorems for Independent Sequences Law of Large Numbers Central Limit Theorem X 1 + X 2 + · · · + X n n EX 1 n →∞ X 1 + X 2 + · · · + X n - nEX 1 nV arX 1 N (0 , 1) n → ∞

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But . ... What happens if the random variables are dependent?
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## This note was uploaded on 04/28/2011 for the course ISEN 609 taught by Professor Klutke during the Spring '08 term at Texas A&M.

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ISEN 609 Lecture 7 - 7 Sequences of Random Variables Most dynamic phenomena are modeled using collections of random variables(measurements over

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