# CT3 An introductory brief and FAQs

CT3 Probability and Mathematical Statistics, as the name suggests, provides a strong base of the statistical concepts and techniques inevitable to any actuarial aspirant. This paper is relatively an easy actuarial exam than others and aspirants usually like to start their actuarial journey with this paper. Let’s peek into this beautiful ‘statistics’ journey, which spans over 3 parts…

### Part 1: The Intro (partly recap!)

The first 3 chapters of the course cover the basic statistical concepts, few of which are taught in school as well. The 3 chapters broadly cover these concepts:

• Basic descriptive statistics concepts such as mean, median, skewness, different data visualization techniques, frequency distributions etc.
• The concept of probability with basic problems to test the understanding
• The concept and properties of a random variable, probability distribution, the distribution function

The next part builds on probability and random variables.

• Chapter 4 (the lengthiest chapter of CT3) delves into the different probability distributions, mainly focussing on their properties and applications.
• Chapters 5,6,7 cover the concepts of generating functions, joint distributions and conditional expectation. They are pretty mechanical and practicing the problems and derivations given in the course notes should suffice.

### Part 3: The show begins here!

This part revolves around inferential statistics i.e. using a random sample of data taken from a
population to describe and make inferences about the population.

• Chapter 8 & 9 gives a brief overview of the concept of sampling, sampling distributions, and the central limit theorem.

The real essence of CT3 can be felt from chapter 10 onwards. Almost 60% of the exam paper is based on topics covered chapter 10 onwards. The next few chapters broadly focus on these 5 areas:

• Point estimation: Use of sample data to calculate a single value (point estimate) of an unknown population parameter. The chapter covers the methods of finding point estimators and their properties.
• Interval estimation: Use of sample data to calculate an interval of possible values of an unknown population parameter. The chapter revolves around finding confidence intervals for various scenarios
• Testing of hypothesis: It is the testing of an assumption about the population parameter by using a sample. The chapter covers the different tests used in different situations.
• Investigating linear relationships between variables using correlation and regression analysis.
• Analysis of variance: The course focuses only on One Way ANOVA, which determines whether there are any statistically significant differences between the means of three or more independent groups

Now that you have a brief idea of what the subject is all about, let’s discuss few questions which are common to many CT3 aspirants…

Q. What is the update to CT3 as per 2019 Curriculum?
The paper will consist of a problem-based assessment using R in addition to a written exam.
In terms of syllabus, few topics such as principal component analysis, generalized linear models, bayesian statistics and bootstrap method have been added.

Q. When should I give CT3?
If you have just started your actuarial journey, then September 2018 is a good option. Owing to the curriculum change, the institute has allowed aspirants to appear for CT3 as a non-member as well. If you have not attempted or have failed to clear CT3, I’ll recommend that you should appear for it in this diet as it’ll be easier to clear it now, as compared to the new syllabus.

Q. How much time is required to complete the syllabus?
The institute recommends 150-200 hours. However, it depends on your educational background (statistics background or any other) as well.

Q. Contrast in difficulty level for a Statistics and a Non-Statistics student
Non-Statistics students usually struggle a bit initially, however, with hard work and practice, the going gets easy. The paper is usually a cakewalk for statistics students.

Q. What should be my preparation strategy for CT3?
A two-step strategy of course notes and revision notes works well for CT3. Also, make a formulae sheet for each chapter so that you have a quick summary to look at while revising and when you get stuck while practicing problems.

Q. What is the average pass percentage of IAI and IFoA?
The pass percentage of IFoA is usually above 60% while for IAI it has been a bit sporadic for the last few diets, varying between 25% to as high as 65%.

Q. What is the passing mark of IAI and IFoA?
The passing mark for IFoA varies from 55 to 60. IAI doesn’t disclose the passing marks, however, it is believed to be around 60.

Q. Is there any additional material which needs to be studied?
The course notes should suffice to get a basic understanding of the concepts. To get a deeper understanding of the theoretical background of the concepts, you can refer to the Fundamentals of Mathematical Statistics by S.C. Gupta and V.K. Kapoor. It covers most of the CT3 concepts.

Like any other actuarial exam, practice is the key to success in the case of CT3 as well. Revise the concepts regularly and practice every day, you’ll definitely ace CT3 like a pro!