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This lecture consists of two
parts that deal with two

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rather different topics.

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In the first part, we look into
an important special case

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of a derived distribution
problem.

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We start with two independent
random variables with known

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distributions and wish to find
the distribution of their sum.

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We will see that for either the
discrete or the continuous

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case, there is a nice formula
that gives us the answer.

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We will develop this formula and
then we will talk a little

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bit about a graphical way
of carrying out the

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calculations involved.

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As we will discuss, this formula
also allows us to

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establish the very important
fact that the sum of two

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independent, normal random
variables is normal.

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In the second part, we introduce
the covariance of

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two random variables and the
correlation coefficient.

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These are certain quantities
that allow us to quantify the

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degree to which two dependent
random variables are related.

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For example, a high value of
the correlation coefficient

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will indicate a strong
relation between

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these random variables.

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We will see the basic
mathematical properties of

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these quantities and provide
some interpretation.

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Later on in this class, we will
see that they play an

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important role in the problem
of estimating one random

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variable, given the
value of another.