Download Review of probability theory

Week Ten – Elements of probability and statistics (events,
sample space, random variables), probability distribution
functions, conditional probabilities
Review of probability and statistics
Context:
Probability theory underlies the study of stochastic processes,
the general subject matter to be covered in the remainder of
the course. We review the basic elements of probability
highlighting conditional probabilities, and discuss two
important distributions: the exponential and Poisson.
Purpose:
To provide you with a refresher on probability
theory, including the sample space, events, random
variables, probability distributions, and the laws of
conditional probability. Several examples are given
to illustrate concepts.
Objectives:
At the end of this lesson, you will be able to:
1. Define the sample space of an experiment
and relate the set of outcomes to the random
variables of interest.
2. Work with conditional probabilities and
Bayes’ theorem.
3. Compute various probabilities associated
with simple experiments such as rolling dice
and flipping coins.
4. Explain the memoryless property of the
exponential distribution and compute
various probabilities of events governed by
the exponential.
5. Explain the relationship between the
exponential distribution and the Poisson
distribution.
6. Work with the Poisson to compute various
probabilities.