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In this lecture, we start our
discussion of continuous

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random variables.

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We will focus on the case of
a single continuous random

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variable, and we'll describe
its distribution using a

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so-called probability density
function, an object that will

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replace the PMFs from
the discrete case.

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We will then proceed to define
the expectation and the

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variance of a continuous random
variable, and we'll see

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that their basic properties
remain unchanged.

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There will be one
new concept--

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the cumulative distribution
function, which will allow us

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to describe, in a unified
manner, both discrete and

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continuous random variables,
even so-called mixed random

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variables that have both
a discrete and

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a continuous component.

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In the course of this lecture,
we will also introduce some of

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the most common continuous
random variables--

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uniform, exponential,
and normal.

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We will pay special attention to
the normal distribution and

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the ways that we can calculate
the associated probabilities.