Unit of study_

# STAT2911: Probability and Statistical Models (Adv)

This unit is essentially an advanced version of STAT2011, with an emphasis on the mathematical techniques used to manipulate random variables and probability models. Common distributions including the Poisson, normal, beta and gamma families as well as the bivariate normal are introduced. Moment generating functions and convolution methods are used to understand the behaviour of sums of random variables. The method of moments and maximum likelihood techniques for fitting statistical distributions to data will be explored. The notions of conditional expectation and prediction will be covered as will be distributions related to the normal: chi^2, t and F. The unit has weekly computer classes where you will learn to use a statistical computing package to perform simulations and carry out computer intensive estimation techniques like the bootstrap method.

Code STAT2911 Mathematics and Statistics Academic Operations 6
 Prerequisites: ? (MATH1X21 or MATH1931 or MATH1X01 or MATH1906 or MATH1011) and a mark of 65 or greater in (DATA1X01 or MATH10X5 or MATH1905 or STAT1021 or ECMT1010 or BUSS1020) None STAT2011

At the completion of this unit, you should be able to:

• LO1. construct appropriate statistical models involving random variables for a range of modelling scenarios. Compute (or approximate with a computer if necessary) numerical characteristics of random variables in these models such as probabilities, expectations and variances
• LO2. fit such models in outcome 1. to data (as appropriate) by estimating any unknown parameters
• LO3. compute appropriate (both theoretically and computationally derived) measures of uncertainty for any parameter estimates
• LO4. assess the goodness of fit (as appropriate) of a fitted model
• LO5. apply certain mathematical results (e.g. inequalities, limiting results) to problems relating to statistical estimation theory
• LO6. prove certain mathematical results (e.g. inequalities, limiting results) used in the course.

## Unit outlines

Unit outlines will be available 2 weeks before the first day of teaching for the relevant session.