Outline

References:

• Ross, A first course in probability
• Ghahramani, Fundamentals of probability

Topics:

1.

Probability Axioms; set functions (unions, intersections, complements); law of total probability; Bayes theorem; conditional probability and independence.

2.

Counting rules; combinations, permutations, multinomial coefficients.

3.

Discrete random variables; probability functions and distribution functions; expected values, variance and standard deviation. Applications and properties of Binomial, Poisson, hypergeometric, geometric models. Finding the distribution of a function of a random variable.

4.

Continuous random variables; density functions and distribution functions; expected values, moments; variance and standard deviation. Properties of normal, uniform, exponential distributions. Finding the distribution of a function of a random variable.

5.

Joint distributions, discrete and continuous; joint pmf and pdf, joint cdf; marginal distributions, conditional distributions; independent random variables; marginal and joint moments; covariance and correlation. Independent random variables and their properties; finding the distribution of functions of random variables, particularly sums of random variables. Specific distributions include the multinomial and bivariate normal distributions.