Class summary:
Monday, 3/10
I first discussed the "maximum/minimum trick", a clever method for
computing the distribution of the maximum or minimum of several
independent random variable. The trick is based on the following
simple observation: the maximum of several numbers x1, x2, ..., is
less than a given bound if and only if each of the numbers x1, x2, ...
is less than this bound. (This idea comes up on p. 316 in the book in
the context of continuous r.v.'s, but it is equally applicable for
discrete r.v.'s.)
I then began Section 3.2 on expectations of r.v.'s.
The expectation, or mean, of a r.v. X, denoted by E(X), is defined in
terms of the distribution of X: E(X) is the sum over x P(X=x), where x
runs over all values of X. E(X) can be interpreted as a weighted
average of the values of X, the weights being the probabilities with
which these values are taken on. I did a few examples in which E(X)
was computed using this definition. A simple, but important example,
was the expectation of an indicator random variable IA,
defined as 1 if A occurs and 0 if A does not occur.
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