WEBVTT
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In this lecture, we continue our
discussion of continuous
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random variables.
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We will start by bringing
conditioning into the picture
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and discussing how the PDF of
a continuous random variable
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changes when we are told that a
certain event has occurred.
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We will take the occasion to
develop counterparts of some
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of the tools that we developed
in the discrete case such as
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the total probability and total
expectation theorems.
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In fact, we will push the
analogy even further.
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In the discrete case, we looked
at the geometric PMF in
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some detail and recognized an
important memorylessness
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property that it possesses.
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In the continuous case, there is
an entirely analogous story
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that we will follow, this time
involving the exponential
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distribution which
has a similar
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memorylessness property.
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We will then move to a second
theme which is how to describe
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the joint distribution of
multiple random variables.
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We did this in the
discrete case by
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introducing joint PMFs.
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In the continuous case, we
can do the same using
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appropriately defined
joint PDFs and by
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replacing sums by integrals.
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As usual, we will illustrate the
various concepts through
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some simple examples and also
take the opportunity to
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introduce some additional
concepts such as mixed random
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variables and the
joint cumulative
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distribution function.