This lecture consists of two parts that deal with two
rather different topics.
In the first part, we look into an important special case
of a derived distribution problem.
We start with two independent random variables with known
distributions and wish to find the distribution of their sum.
We will see that for either the discrete or the continuous
case, there is a nice formula that gives us the answer.
We will develop this formula and then we will talk a little
bit about a graphical way of carrying out the
calculations involved.
As we will discuss, this formula also allows us to
establish the very important fact that the sum of two
independent, normal random variables is normal.
In the second part, we introduce the covariance of
two random variables and the correlation coefficient.
These are certain quantities that allow us to quantify the
degree to which two dependent random variables are related.
For example, a high value of the correlation coefficient
will indicate a strong relation between
these random variables.
We will see the basic mathematical properties of
these quantities and provide some interpretation.
Later on in this class, we will see that they play an
important role in the problem of estimating one random
variable, given the value of another.