1
STAT 5112
Spring 2012
Lecture 9
Jan 30, 2012
Jun Xie
Review the Bayes
’
theorem and go over examples.
2.5 Independence
Definition
Two events
A
and
B
are
independent
if
P
(
A

B
) =
P
(
A
) and are
dependent
otherwise.
Proposition
A
and
B
are independent if and only if (iff)
P
(
A
B
) =
P
(
A
)
P
(
B
)
Example 34
It is
known that 30% of a certain company’s washing machines require service while under
warranty, whereas only 10% of its dryers need such service. If someone purchases both a washer and a
dryer made by this company, what is the probability that both machines will need warranty service?
Definition
Events
A
1
, . . . ,
A
n
are
mutually independent
if for every
k
(
k
= 2, 3, . . . ,
n
) and every subset of indices
i
1
,
i
2
, . . . ,
i
k
,
Example 36
Solar photovoltaic system
Consider a particular lifetime value
t
0
, and suppose we want to determine the probability that the
system lifetime exceeds
t
0
. Let
A
i
denote the event that the lifetime of cell
i
exceeds
t
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 Fall '08
 BUD
 Probability theory, Cumulative distribution function

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