Probability & Statistics II
Resources for Probability & Statistics II - for more information about the courses, please see course outlines.
MLC Drop-In Centre
Students from Probability & Statistics II can use the drop-in centre, but we will give priority to first year students. If you see every other table has students, then we would appreciate it if you found another place to sit so that there is room for new students.
Please note that not every staff member in the MLC knows all of the content in Probability & Statistics II, there will be times when we can only give general study advice for this course.
Assumed knowledge
These resources can help you revise assumed knowledge for probability and statistics. The various topics in the course are taught assuming you know this information.
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Integration
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.
This PDF document contains many written worked examples of various techniques of integration.
This lecture for the old MLC Bridging Course MathsTrack is on the fundamental techniques of integration.
- Integration lecture: integration techniques (YouTube)
- Integration lecture: integration techniques handwritten notes (PDF)
This seminar was given for Maths 1A in Sem 1 2021 and began with integration by just doing it, substitution and integration by parts.
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Sums and series
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 1A Sem 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.
- Revision seminar: sum notation, Sem 1 2016 (YouTube)
- Revision seminar notes: sum notation Sem 1 2016 (PDF)
This handout lists the useful finite and infinite series you need to be familiar with for theoretical calculations.
This seminar for Maths 1B in 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.
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First year statistics
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 for students 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.)
- Revision seminar: Stat Prac I: probability, 2013 (YouTube)
- Revision seminar notes: Stat Prac I: probability 2013 (PDF)
This revision seminar was given in for students of Business and Economic Statistics in 2015 and various ideas about probability including a discussion of how to think about probability using variables, and the meaning of disjoint and independent.
Topics in Probability & Statistics II
These revision seminars from various courses are useful for studying or revising Probability & Statistics II. Note that this course has changed a few times over the years, and even if the content is roughly the same, each new lecturer has a slightly different emphasis, which means that the older seminars may not match the current content exactly.
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Counting techniques
This revision seminar was given for students in Probability & Statistics II in Semester 1 2024. David discussed many ideas relating to counting techniques at the start.
- Revision seminar section: Prob & Stats II: counting 2024 (YouTube)
- Revision seminar notes: Prob & Stats II: counting 2024 (PDF)
This revision seminar was given to students of Mathematics for Information Technology in 2012. It covered counting techniques, including combinations, permutations, allocations etc.
- Revision seminar: Maths for IT: counting techniques 2012 (YouTube)
- Revision seminar notes: Maths for IT: counting techniques 2012 (PDF)
This revision seminar was given for students of Mathematics for Data Science in Semester 2 2020. David discussed counting strategies, including the multiplication principle, and permutations and combinations.
- Revision seminar: Maths for Data Science: counting techniques 2020 (YouTube)
- 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).
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Probability distributions
This revision seminar was given in 2018 for students in Engineering Maths IIA. David 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.)
- Revision seminar: Eng Maths IIA: distributions 2018 (YouTube)
- Revision seminar notes: Eng Maths IIA distributions 2018 (PDF)
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 calculating with poisson and exponential distributions.
- Revision seminar section: Prob & Stats II: Poisson processes 2019 (YouTube)
- Revision seminar notes: Prob & Stats II: Poisson processes (PDF)
This revision seminar given in Sem 1 2018 to Probability & Statistics II students had a section (starting at 49m5s) on Poisson processes, with several examples of calculating probabilities with poisson and exponential distributions.
- Revision seminar section: Prob & Stats II: Poisson processes 2018 (YouTube)
- Revision seminar notes: Prob & Stats II: Poisson processes 2018 (PDF)
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).
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Multivariate distributions
This seminar for Probability & Statistics II students in semester 1 2016, was on 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.
- Revision seminar: Prob & Stats II: bivariate distributions 2016 (YouTube)
- Revision seminar notes: Prob & Stats II: bivariate distributions 2016 (PDF)
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.
- Revision seminar section: Prob & Stats II: multivariate distributions 2021 (YouTube)
- No notes available for 2021 seminars
This seminar for Probability & Statistics II students in semester 1, 2018, had a section on bivariate distributions (starting at 1h28m20s). David talked through some of the ideas and did a couple of examples.
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Probability generating functions and moment generating functions
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.
This seminar for Probability & Statistics II students in Semester 1 2018 started with a section on probability generating functions.
- Revision seminar section: Prob & Stats II: PGFs 2018 (YouTube)
- Revision seminar notes: Prob & Stats II: PGFs 2018 (PDF)
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.
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Markov chains
This seminar for Probability & Statistics II students in Semester 1 2021 ended with a section on Markov chains (starting at 1h27m14s).
- Revision seminar section: Prob & Stats II: Markov chains 2021 (YouTube)
- 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.
- Revision seminar: Prob & Stats II: Markov chains with absorbing states 2016 (YouTube)
- Revision seminar: Prob & Stats II: Markov chains with absorbing states 2016 (PDF)
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).
- Revision seminar section: Prob & Stats II: various problems 2022 (YouTube)
- Revision seminar notes: Prob & Stats II: Markov chain equilibrium probabilities 2022 (PDF)
In this revision seminar for Probability & Statistics II in Semester 1 2024, David ended by discussing finding equilibrium probabilities of a Markov chain with infinitely many states.
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Proofs and order statistics
This seminar for Probability & Statistics II students in Semester 1 2019 began with a section on order statistics and calculating distributions for them.
- Revision seminar section: Prob & Stats II: order statistics 2019 (YouTube)
- Revision seminar notes: Prob & Stats II: order statistics 2019 (PDF)
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.
- Revision seminar: Prob & Stats II: proofs 2019 (YouTube)
- Revision seminar notes: Prob & Stats II: proofs 2019 (PDF)
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.
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Revision seminars in order of time
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.)
2025
This revision seminar was given for students in Probability & Statistics II in Semester 1 2025. David discussed the following topics: probability calculations with Markov chains (at the beginning); moment generating functions (starting at 28m24s); methods for finding PDFs such as the CDF method and the transformation method (starting at 1h16m10s). Note there is a mistake at 1h23m23s where he differentiated something with an exponent of n and got an exponent of n in his answer, but the new exponent should have been n-1. The correct expression is in the notes, though.
- Revision seminar video: Prob & Stats: markov chains, mgfs, finding pdfs 2025 (YouTube)
- Revision seminar notes: Prob & Stats: markov chain calculations 2025 (PDF)
- Revision seminar notes: Prob & Stats: moment generating functions 2025 (PDF)
- Revision seminar notes: Prob & Stats: methods for finding pdfs 2025 (PDF)
2024
This revision seminar was given for students in Probability & Statistics II in Semester 1 2024. David discussed many ideas relating to counting techniques, and then (starting at 1h14m20s), he did an example of finding equilibrium probabilities in a Markov chain with infinitely many states.
- Revision seminar video: Prob & Stats II: counting and infinite Markov chains 2024 (YouTube)
- Revision seminar notes: Prob & Stats II: counting 2024 (PDF)
- Revision seminar notes: Prob & Stats II: infinite Markov chains 2024 (PDF)
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.
- Revision seminar video: Prob & Stafs II: Poisson processes 2023 (YouTube)
- Revision seminar notes: Prob & Stats II: Poisson processes 2023 (PDF)
- Revision seminar notes: Prob & Stats II: Counting 2023 (PDF)
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).
- Revision seminar: Prob & Stats II: various problems 2022 (YouTube)
- Revision seminar notes: Prob & Stats II: probability bounds 2022 (PDF)
- Revision seminar notes: Prob & Stats II: combining variables 2022 (PDF)
- Revision seminar notes: Prob & Stats II: Markov chain equilibrium probabilities 2022 (PDF)
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, 1h27m14s, it ended with a section on Markov chains.
- Revision seminar: Prob & Stats II: multivariate distributions and Markov chains 2021 (YouTube)
- 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, then David talked about Poisson processes including the Poisson and exponential distributions (starting at 1h5m20s) and counting (starting at 1h36m40s).
- Revision seminar: Prob & Stats II: order statistics, poisson processes, counting 2019 (YouTube)
- Revision seminar notes: Prob & Stats II: order statistics 2019 (PDF)
- Revision seminar notes: Prob & Stats II: poisson processes 2019 (PDF)
- Revision seminar notes: Prob & Stats II: counting 2019 (PDF)
The above seminar for Probability & Statistics II in Semester 1 2019 continued in a separate video. 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.
- Revision seminar: Prob & Stats II: proofs 2019 (YouTube)
- Revision seminar notes: Prob & Stats II: proofs 2019 (PDF)
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)..
- Revision seminar: Prob & Stats II: PGFs, poisson processes and bivariate distributions 2018 (YouTube)
- Revision seminar notes: Prob & Stats II: probability generating functions 2018 (PDF)
- Revision seminar notes: Prob & Stats II: poisson processes 2018 (PDF)
- Revision seminar notes: Prob & Stats II: bivariate distributions 2018 (PDF)
2016
This seminar for Probability & Statistics II students in semester 1 2016, was on 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.
- Revision seminar: Prob & Stats II: bivariate distributions 2016 (YouTube)
- Revision seminar notes: Prob & Stats II: bivariate distributions 2016 (PDF)
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.
- Revision seminar: Prob & Stats II: Markov chains with absorbing states 2016 (YouTube)
- Revision seminar notes: Prob & Stats II: Markov chains with absorbing states 2016 (PDF)
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.