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In this lecture, we introduce
and develop the concept of

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independence between events.

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The general idea is
the following.

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If I tell you that a certain
event A has occurred, this

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will generally change the
probability of some other

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event B. Probabilities will
have to be replaced by

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conditional probabilities.

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But if the conditional
probability turns out to be

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the same as the unconditional
probability, then the

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occurrence of event A does not
carry any useful information

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on whether event B will occur.

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In such a case, we say that
events A and B are

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independent.

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We will develop some intuition
about the meaning of

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independence of two events and
introduce an extension, the

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concept of conditional
independence.

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We will then proceed to define
the independence of a

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collection of more
than two events.

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If, for any two of the events
in the collection we have

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independence between them, we
will say that we have pairwise

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independence.

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But we will see that
independence of the entire

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collection is something
different.

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It involves additional
conditions.

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Finally, we will close with an
application in reliability

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analysis and with a nice puzzle
that will serve as a

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word of caution about putting
together probabilistic models.