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In order to do many of the calculations in this course, you need to be familiar with definite integrals, especially doing substitution and integration by parts. These resources will help you revise.

This table of derivatives is useful for recognising when you can just do an integral.

• Table of derivatives (PDF handout)

This PDF document contains many written worked examples of various techniques of integration.

• Techniques of integration worked examples (PDF booklet)

This lecture for the old MLC Bridging Course MathsTrack is on the fundamentalÌýtechniques of integration.

This seminar was givenÌýfor Maths 1A in Sem 1 2021 and began with integration by just doing it, substitution and integration by parts.

Various calculations in this course require you to work with sum notation and be familiar with various infinite series. These resources will help you revise this content.

This seminar for Maths 1AÌýSem 1 2016 discussed how sum notation works, the rules for how it interacts with other operations, and some of the special manipulations you can do with it.

This handout lists the useful finite and infinite series you need to be familiar with for theoretical calculations.

• Useful series for probability handout (PDF)

This seminar for Maths 1BÌýin Summer Semester 2019 ended with a section on infinite series examples (starting at 1h30m), and it contains many of the skills you need for the calculations in Probability & Statistics II.

This course is taught assuming you have seen some of the concepts of probability distributions before, such as means and standard deviations, probability laws, and the binomial and normal distributions.

This seminar was given forÌýstudents in Statistical Practice I in 2013. It was mainly about probability and distributions, including types of variables, probability distributions, theoretical means and standard deviations and probability laws. (It also included a little on how to choose what hypothesis test goes with what situation, as well as the chi-squared test.)

This revision seminar was given in for students ofÌýBusiness and Economic Statistics in 2015 andÌývarious ideas about probability including a discussion of how to think about probability using variables, and the meaning of disjoint and independent.ÌýÌý

This revision seminar was given to students ofÌýMathematics for Information Technology in 2012. It covered counting techniques, including combinations, permutations, allocations etc.

This revision seminar was given for students of Mathematics for Data ScienceÌýin Semester 2 2020. David discussed counting strategies, including the multiplication principle, and permutations and combinations.

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• No notes available from 2020 seminars

This revision seminar was given to students of Probability & Statistics II in 2019 and it has a section on counting (starting at 1h36m40s).

This revision seminar was given in 2018 for students in Engineering Maths IIA.ÌýDavid discussed all of the distributions appearing in Eng Maths IIA in turn, including how to decide which distribution you want to use and how to use it. (All of these distributions are covered in Prob & Stats II, though there are some distributions in Prob & Stats II that aren't in this seminar.)

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This revision seminar given in 2019 for students in Probability & Statistics II had a section (starting at 1h5m20s) on Poisson processes, where David went through several examples of calculatingÌýwith poisson and exponential distributions.Ìý

This revision seminar given in Sem 1 2018 to Probability & Statistics II students had a section (starting at 49m5s) on Poisson processes,Ìýwith several examples of calculating probabilities with poisson and exponential distributions.

In the middle section of this revision seminar for Probability & Statistics II in Semester 1 2022, David several problems involving making new variables out of old ones including minimums (starting at 43m27s).

This seminar for Probability & Statistics II students in semester 1 2016, wasÌýon bivariate distributions, specifically focussing on the decisions that need to be made in order to choose limits for integrals. David did three examples including finding the integral of the whole distribution, finding a probability, and finding a marginal distribution.

This seminar for Probability & Statistics II in Semester 1 2021 began with a section on multivariate distributions, including conditional and marginal distributions and the multinomial distribution.

• No notes available for 2021 seminars

This seminar for Probability & Statistics II students in semester 1, 2018, hadÌýa section on bivariate distributions (starting atÌý1h28m20s).ÌýDavid talked through some of the ideas and did a couple of examples.

This handout lists the useful finite and infinite series you need to be familiar with in order to do the calculations involved with moment generating functions and probability generating functions.

• Useful series for probability handout (PDF)

This seminar for Probability & Statistics II students in Semester 1 2018 started with a section on probability generating functions.

This short seminar for Probability & Statistics II students in Semester 1 2016 was about moment generating functions, including examples with both a discrete distribution and a continuous distribution.

This seminar for Probability & Statistics II students in Semester 1 2021 ended with a section on Markov chains (starting at 1h27m14s).

• No notes available from 2021 seminars

This seminar for Probability & Statistics II students in Semester 1 2016 was about Markov chains with absorbing states, including rearranging the transition matrix to get a block triangular matrix.

In this revision seminar for Probability & Statistics II in Semester 1 2022, David ended by discussing finding equilibrium probabilities for a Markov chain (starting at 1h25m).

This seminar for Probability & Statistics II students in Semester 1 2019 began with a section on order statistics and calculating distributions for them.Ìý

This seminar for Probability & Statistics II students in Semester 1 2019 was about proofs. David discussed a few proofs, trying to prove Chebychev's inequality without having seen it (and needing help), successfully proving Markov's inequality without having seen the proof, and proving a formula for variance with iterated expectations.

In this revision seminar for Probability & Statistics II in Semester 1 2022, David started by discussing several problems involving finding bounds on probabilities using theorems like Markov's and Chebychev's inequalities.Ìý

These are the revision seminars that have been given for Probability & Statistics II over the years, with the newest seminars at the top. (Note in the topic-specific sections above, there are a few seminars from other courses that you might also find relevant.)

2023

This revision seminar was given for students in Probability & Statistics II in Semester 1 2023. David discussed Poisson processes and also counting problems, but the recording was corrupted at about 20 minutes in before getting to counting problems. You can still see the notes for both sections below.

2022

In this revision seminar for Probability & Statistics II in Semester 1 2022, David discussed various problems given by the students. First there were several problems involving finding bounds on probabilities, then there were several problems involving making new variables out of old ones including minimums (43m27s), then there was a problem finding equilibrium probabilities for a Markov chain (1h25m).

2021

This seminar for Probability & Statistics II in Semester 1 2021 began with a section on multivariate distributions, including conditional and marginal distributions and the multinomial distribution. After this,Ìý1h27m14s, it endedÌýwith a section on Markov chains.

• No notes available from 2021 seminar

2019

This seminar for Probability & Statistics II students in Semester 1 2019 began with a section on order statistics and calculating distributions for them, thenÌýDavid talked aboutÌýPoisson processes including the Poisson and exponential distributions (starting at 1h5m20s) and counting (starting at 1h36m40s).

The above seminar for Probability & Statistics II in Semester 1 2019 continued in a separate video.ÌýDavid discussed a few proofs, trying to prove Chebychev's inequality without having seen it (and needing help), successfully proving Markov's inequality without having seen the proof, and proving a formula for variance with iterated expectations.

2018

This seminar for Probability & Statistics II students in Semester 1 2018 covered probability generating functions, poisson processes (starting at 49m5s) and some ideas about bivariate distributions (starting at 1h28m20s)..

2016

This seminar for Probability & Statistics II students in semester 1 2016, wasÌýon bivariate distributions, specifically focussing on the decisions that need to be made in order to choose limits for integrals. David did three examples including finding the integral of the whole distribution, finding a probability, and finding a marginal distribution.

This seminar for Probability & Statistics II students in Semester 1 2016 was about Markov chains with absorbing states, including rearranging the transition matrix to get a block triangular matrix.

This short seminar for Probability & Statistics II students in Semester 1 2016 was about moment generating functions, including examples with both a discrete distribution and a continuous distribution.