**Course Objectives:** | The course will cover the axioms of probability, conditional probability and
independence. Students will be expected to understand discrete and continuous random
variables and the independence of random variables. Students should also understand
the concept of conditional expectation, the laws of large numbers and the central
limit theorem. Depending on instructor students may encounter probabilistic coding
theory and entropy. |

**Topical Outline:** | 1. Basic counting principles and combinatorial coefficients.
2. Sample spaces and axioms for probability.
3. Conditional probability, Bayes' formula, independent events.
4. Random variables and expectation, binomial distribution,
Bernoulli and Poisson
random variables.
5. Continuous random variables, expectation, variance. Normal
random variables,
other continuous distributions such as exponential, gamma,
Cauchy, beta.
6. Jointly distributed random variables.
7. Properties of expectation, expectation of the sum of random
variables,
conditional expectation, variance and covariance.
8. Limit theorems: Weak law of large numbers, strong law of large
numbers, central
limit theorem. |