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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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View Full Document 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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...
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.
 Spring '08
 Klutke

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