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In this lecture, we
introduce the

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notion of a random variable.

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A random variable is, loosely
speaking, a numerical quantity

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whose value is determined by the
outcome of a probabilistic

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experiment.

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The weight of a randomly
selected

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student is one example.

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After giving a general
definition, we will focus

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exclusively on discrete
random variables.

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These are random variables that
take values in finite or

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countably infinite sets.

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For example, random variables
that take

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integer values are discrete.

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To any discrete random variable
we will associate a

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probability mass function, which
tells us the likelihood

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of each possible value of
the random variable.

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Then we will go over a few
examples and introduce some

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common types of random
variables.

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And finally we will introduce
a new concept- the expected

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value of the random variable,
also called the

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expectation or mean.

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It is a weighted average of
the values of the random

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variable, weighted according
to their respective

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probabilities, and has an
intuitive interpretation as

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the average value we expect to
see if we repeat the same

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probabilistic experiment
independently a

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large number of times.

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Expected values play a central
role in probability theory.

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We will look into some
of their properties.

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And we will also calculate the
expected values of the example

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random variables that we
will have introduced.