**Subject Code/Name:** MTH2232 - Mathematical Statistics (note: I suggest reading this in tandem with my review for MTH2222,

here)

**Workload:**- 3x1 Hour Lectures
- 1x2 Hour Tutorial

**Assessment:**- Weekly Homework (12%)
- 3 Assignments (12% all up)
- Mid-semester Test (6%)
- Examination (70%)

**Recorded Lectures:** Yes, with screen capture/blackboard recording.

**Past exams available:** Yes, three available with solutions. However, one of these wasn't very relevant to the unit.

**Textbook Recommendation:** Probability & Statistical Inference 8ed PNIE, Hogg R (Recommended)

Honestly - I LOVED this textbook. I originally had it borrowed from the library, but I loved it so much that I actually went out and bought it. (Note, I got it off of fishpond for $60 as opposed to Monash's price of $116.51)

**Lecturer(s):**- Pavel Chigansky
- Kais Hamza

Pavel was... Not my favourite lecturer, to say the least. He got sidetracked a lot early on, and so when we got to the end of week 4 he had to rush through all the content. Unfortunately, the content that he rushed through is the single most important content in the whole unit (NOT an understatement. You'll see why later)

Kais, I have nothing but love for. He felt we were so far behind at one point, he actually spent a whole week to consolidate information, cancelling the week's assessment. Seriously, he is an amazing man.

**Year & Semester of completion:** 2014, Semester 2

**Rating:** 5 out of 5

**Your Mark/Grade:** 90, HD

Don't let the higher mark than MTH2222 fool you - I would rate this as higher in difficulty. The marks only reflect how much more enjoyable I found this over MTH2222, rather than a reflection on difficulty.

**Comments:** This unit is (from what I could tell) actually very similar to STA1010. The reason for that is quite simple, though - STA1010 is a unit to teach statistical methods that are very useful for one in the sciences. MTH2232, however, is designed so that one can create these statistical tests. As such, a lot of the content is similar, however in MTH2232 you are expected to be able to derive any form of statistical test through what you've learned. Funnily enough, MTH2232 and STA1010 aren't prohibitions - means you can get a nice bludge if you do MTH2232 first. (and I do often help my friends with STA1010, so there is a lot of relevance). MTH2232 can be broken up into three sections, like so:

1. ProbabilityThis section is a doozy - basically, to do statistical inference, you need to understand probability. This is because probability is the language of statistical inference. So, you spend the first four weeks in intense work, learning about all the necessary skills. It's basically 2/3 of the MTH2222 course condensed into four weeks - minus limit theorems (except Central Limit Theorem) and some of the bits from section 4. We also don't have the time to extend all the different techniques to the distributions we know as a result.

Something that is done, however, is we consider three "extra" distributions - the chi-squared distribution, which is a special case of the gamma distribution, and the F and t-distributions. The latter 2 just randomly pop up for no reason in chapter 5's content, however it makes sense very quickly why we considered them. There is a much heavier emphasis on the transformations of random variables in this unit.

Finally, the most important content of the whole unit is in section - often referred to as "chapter 5" (since this is where the content is in the textbook). This is no understatement, either - EVERYTHING you learn in chapter 5 is ESSENTIAL to later parts of the unit, whereas earlier chapters are only really necessary so that you can understand chapter 5 and play around with populations.

2. Statistical TestsThis is the bulk of the unit, and can be further separated into two parts - confidence intervals and hypothesis testing.

There's not really much else to say - you consider how to create confidence intervals using the content from chapter 5, and do this for a bunch of different cases. For means, variances, proportions, and you also consider the optimal sample sizes for different situations.

Hypothesis testing then extends on from confidence intervals, but you also consider hypothesis tests for other situations, such as when you have m different sets of n samples. (ANOVA tables)

The proofs from this section are often hard to follow, but nothing a good sit-down and looking at can't help.

3. Other thingsI can't comment too much on this - Kais said he wanted to go over some "very nice" results from chapter 10 (the chapter is literally titled "Some Theory"), but we ran out of time. We did go over chi-squared tests, which are designed to check lots of different things. One thing they can do is check how well a distribution fits to a sample (which is why the tests are often called "chi-squared goodness-of-fit tests). These particular tests are based the multinomial distribution, which is some new theory to add on from section 1.

On the Exam...One thing I wanted to highlight special is that this unit's exam is different to many other unit's exams. Firstly, you don't get a scientific calculator like in STA1010. Secondly, you're allowed a double sided summary sheet which you can take into the exam (we were also allowed this for the mid-sem). Thirdly, it's split up into two sections, but these two sections don't work like many other units. Unlike in most units, where it's a case of "here's the content from weeks 1-6, and here's the content from weeks 7-12". Rather, section A is a "Theory" section, in which you need to be able to derive your own statistical tests (as well as some minor probability questions, nothing like MTH2222 though), and section B is an "Application" section. Unlike in section A, for section B you're allowed to just blindly use formula without any explanation as to why (much like how I'd expect STA1010 to be).

In terms of MTH2222, the crossover was very nice. For the most part, it made MTH2222 a lot easier because I had already seen the material (I nearly started skipping lectures altogether for MTH2222 as a result, and sometimes did skip the lecture because I knew what was coming), but near the end it helped consolidate what I'd learned in MTH2232 (this was probably due to the rush at the end, though).

I found MTH2232 to be a lot more fun that MTH2222, however MTH2222 was obviously much more necessary for future probability/statistics units. Same advice from my other review if you're unsure of which to pick.