# Actuarial Science CS1 An Introductory Brief

In this article, we will discuss about Actuarial Science CS1. CS1-Actuarial Statistics 1, as the name suggests, provides a strong base of the statistical concepts and techniques inevitable to any actuarial aspirant. The paper will be evaluated at 2 levels: A theory exam (CS1A) which will be weighted at 70% and a computer-based exam (CS1B), which involves solving problems using R, will be weighted at 30%.

CT3 has been transferred to CS1 under Curriculum 2019 and there aren’t any drastic changes in the previous syllabus, but there has been a significant increase in the length and breadth of this paper due to the inclusion of new topics. Few topics, which were previously covered in CT6 have been added to this paper in addition to a few new topics.

Almost 70% of the syllabus is the same if you have studied CT3. Almost 30% of things are new! IFoA has divided the new syllabus into 5 parts, as shown in Figure 1. Let’s have a look at what’s in store for us in this
new journey! ### Part 1: Random Variables and Distributions

This part can be broadly divided into 3 sections:

• The concept of random variables: Random (associated with a probability) variable (it takes different values). To put it neatly, it is a variable whose value is subject to variations due to chance.
• It then delves into the different probability distributions, which are mathematical functions that provide the probabilities of occurrence of different possible outcomes in an experiment and mainly focusses on their properties and applications probability distributions.
• It also covers the concepts of generating functions, which are a neat way of working out various properties of probability distributions without having to use integration repeatedly.

### Part 2: Data Analysis

This part covers the basic exploratory data analysis which every analyst usually does on a dataset to understand what the data wants to speak. It covers everything about the descriptive statistics, right from making frequency distributions to understanding the skewness for the distribution of a dataset. A new addition to this section is a widely used method of data reduction: Principal Component Analysis. This part also focusses on the concept of sampling, sampling distributions, and central limit theorem.

### Part 3: Statistical Inference

This part focusses on learning characteristics of the population from a sample. It can be broadly divided into 3 sections:

• 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. An addition to the old (CT3) syllabus is the use of the Bootstrap method to estimate properties of an estimator.
• 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. An addition to the old (CT3) syllabus is the use of the Bootstrap method to obtain confidence intervals.
• 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. An addition to the old (CT3) syllabus is the concept of applying the permutation approach to non-parametric hypothesis tests.

### Part 4: Regression Theory and Applications

This part has been divided into 2 sections: Linear Regression and Generalized Linear Models.

• Regression Analysis: It covers the basic theory of regression i.e, a technique for determining the statistical relationship between two or more variables where a change in a dependent variable is associated with, and depends on, a change in one or more independent or explanatory variables. It focusses on simple (one independent variable) and multiple (more than one independent variable) linear regression. A
major part of the syllabus here focusses on applying the concept using R. An addition to the old (CT3) syllabus is the use of measures of model fit to select an appropriate set of explanatory variables.
• Generalized Linear Models (GLM): It is a flexible generalization of ordinary linear regression that allows for response variables that have error distribution models other than a normal distribution. This concept was covered in CT6 and has now been transferred to CS1.

### Part 5: Bayesian Statistics

Like GLM, this concept was also covered in CT6 and has now been transferred to CS1. It mainly focusses on the fundamental concepts of Bayesian statistics and using these concepts to calculate Bayesian estimators. It can be divided into 2 parts:

• Bayes’ theorem, which describes the probability of an event, based on prior knowledge of conditions that might be related to the event. It also focusses on concepts of prior, posterior and conjugate prior distribution.
• Credibility theory: When you have multiple estimates of a future event, and you would like to combine these estimates in such a way to get a more accurate and relevant estimate. It mainly focusses on the Bayesian approach and Empirical Bayes approach to credibility theory.

The above 5 areas will be covered in the theory exam (CS1A), which will be a standard pen-paper exam and the computer-based exam (CS1B), which will be done in R. The institute has not drawn a strict line between the topics for the theory exam and the practical exam as it focusses on applying the theoretical concepts using R. The main topics which can be applied using R are exploratory data analysis, calculating probabilities and quantiles associated with distributions, point, and interval estimation, hypothesis testing and regression analysis.

As the paper focusses on theory and its applications using R, a two-step strategy of studying the concept and solving problems manually and then solving it using R will help in understanding the concept in detail and preparing well for the exam. For practice, you can refer to past CT3 papers and try exploring those problems in R as well. The institute has also provided specimen papers, which can serve as mock papers before the final exam.

Studying for this paper will definitely build a strong base for your actuarial journey, as it has been beautifully woven, combining few parts of CT6 and introducing few new concepts, which will prove to be helpful at work as well as in preparations of further exams.