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

Info iconThis preview shows pages 1–5. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 , . . .
Background image of page 2
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 → ∞
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
But . ... What happens if the random variables are dependent?
Background image of page 4
Image of page 5
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 9

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

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online