Class summary:
Wednesday, 4/23
I started out with a brief review of the Poisson process example from
Monday's class and discussed a variation of the last question in
this example, namely the probability that the 100th customer
arrives within 12 hours of the opening of the store. This amounts to
computing a probability associated with a sum of a large number of
i.i.d. random variables (namely the W_i's), so normal approximation
can be applied to compute (approximately) this probability.
I then began the final topic of this class, joint continuous
distributions. Most of this material can be found in Sections 5.1-5.3
of the Pitman text. I passed out two handouts:
- Joint continuous distributions.
A summary of definitions, properties, and formulas (most of which are
analogous to the discrete case which came up in Chapter 3).
- Double integrals. A set of tips and
practice on double integrals, focusing on those types of integrals are
frequently occur in probability computations.
A Solution Sheet to the practice
problems is also available.
I began a series of examples illustrating the use of these formulas,
which I will continue for another hour or two.
Exam 3: The final hour exam will be Friday, May 2. It will
include the material covered since the last exam through the end of
Chapter 4 (but not Chapter 5).
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