Instructor

* wperkins3@math.gatech.edu*

Office: Skiles 017

Office Hours: Thursday 11 am - 1pm, or by appointment

Topics

- Sections: 1.1 - 1.5, 2.1, 2.3, 2.5, 3.1, 3.2, 3.5, 4.1
- Definitions:
- Probability Space
- Field, Sigma Field
- Probability Measure
- Conditional Probability
- Independent Events
- Random Variable
- Distribution Function
- Indicator Random Variable
- Discrete Random Variable
- Probability Mass Function
- Continuous Random Variable
- Probability Density Function
- Random Vector
- Joint Distribution Function
- Independent Random Variables
- Discrete Random Variables: Bernoulli, Poisson, Binomial, Geometric
- Continuous Random Variables: Uniform, Normal, Exponential

- Theorems: 1.3.4, 1.3.5, 1.4.4, 2.1.6, 2.5.5, 4.2.3
- Sample Questions:
- Are there random variables which are neither discrete nor continuous? If so, give an example.
- Give an example of a field that is not a sigma field.
- Show that the sum of two independent Poisson rv's is a Poisson.
- Give an example of a collections of rv's that are pairwise independent but not jointly independent.
- Calculate the probability that the sum of k independent exponential rv's with mean 1 is less than 1.
- On the set of outcomes {1, 2, ... n} give three different sigma fields.
- Say two probability spaces share the same outcome space and sigma field, but have different probability functions. Are the same events independent in both spaces? Why or why not?