Statistics 241/541: Probability Theory
YALE UNIVERSITY, FALL 1995
Prof. Nicolas Hengartner
This course serves for an introduction to probability theory,
for students who have had calculus (but not advanced calculus
or measure theory). It serves as prerequisite for Statistics 242.
The course emphasizes the aspects of probability theory that are
needed to use probability models in applications. The material
is presented from the concrete to the abstract.
Students should take away from this course the following:
- Probability spaces as models for chance experiments; the
probability of an event as a quantity representing its
long-run relative frequency
- The notion of random variable: a function on an outcome set,
used to model a quantity determined by the outcome of a
- The expected value of a random variable, representing its
expected long-run average value .
- The limit theorems: weak law of large numbers, strong law of
large numbers and the central limit theorem.
- The idea of a distribution as an assignment of probability
to intervals, and thence to sets that can be made from intervals
by set operations; the distribution of a random variable.
- The two main kinds of distributions: discrete and absolutely continuous,
and the various kinds of calculations involving them.
- The standard "brand-name" distributions and models most used in
practice, including the Poisson process.
- Joint, marginal and conditional distributions.
- Distribution theory: finding the distribution of a function
of one or more random variables; including the use of
probability generating functions.
- Conditional probability and independence; the use of conditioning
and Bayes's Theorem.
Introduction to Probabily, D.G. Kelly, MacMillan press, 1994.
The grades are made-up by:
- Weekly assignments counting for 30% (Do them!)
- One midterm counting for 30 %
- One in class final counting for 40 %.