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# MAS-I Exam Syllabus Modern Actuarial Statistics : Casualty Actuarial Society

Organisation : Casualty Actuarial Society
Name Of The Exam : Modern Actuarial Statistics – I MAS
Announcement : Syllabus

## MAS-I Exam Syllabus :

Learning Objectives set forth, usually in broad terms, what the candidate should be able to do in actual practice.

Related : AEEE Syllabus Amrita Engineering Entrance Exam Amrita University : www.syllabus.gen.in/911.html

Included in these learning objectives are certain methodologies that may not be possible to perform on an examination, such as calculating the Hat Matrix for a complex Generalized Linear Model, but that the candidate would still be expected to explain conceptually in the context of an examination.

Knowledge Statements identify some of the key terms, concepts, and methods that are associated with each learning objective.

These knowledge statements are not intended to represent an exhaustive list of topics that may be tested, but they are illustrative of the scope of each learning objective.

Readings support the learning objectives. It is intended that the readings, in conjunction with the material on earlier examinations, provide sufficient resources to allow the candidate to perform the learning objectives.

Some readings are cited for more than one learning objective. The CAS Syllabus & Examination Committee emphasizes that candidates are expected to use the readings cited in this Syllabus as their primary study materials.

A. Probability Models (Stochastic Processes and Survival Models)
Learning Objectives :
1. Understand and apply the properties of Poisson processes :
** For increments in the homogeneous case
** For interval times in the homogeneous case

** For increments in the non-homogeneous case
** Resulting from special types of events in the Poisson process
** Resulting from sums of independent Poisson processes

Knowledge Statements :
a. Poisson process
b. Non-homogeneous Poisson process

c. Memory less property of Exponential and Poisson
d. Relationship between Exponential and Gamma
e. Relationship between Exponential and Poisson

2. For any Poisson process and the inter-arrival and waiting distributions associated with the Poisson process, calculate :
** Expected values
** Variances
** Probabilities

Knowledge Statements :
a. Probability calculations for Poisson process
b. Conditional distribution of arrival times

c. Splitting grouped Poisson rate to subsets of population using probability distribution
d. Conditional distribution of events by category within a group within a certain time period

3. For a compound Poisson process, calculate moments associated with the value of the process at a given time.

Knowledge Statements :
a. Compound Poisson process mean and variance
b. Normal approximation and hypothesis testing
Range of weight : 0-5 percent

4. Apply the Poisson process concepts to calculate the hazard function and related survival model concepts.

** Relationship between hazard rate, probability density function and cumulative distribution function
** Effect of memory less nature of Poisson distribution on survival time estimation

Knowledge Statements :
a. Failure time random variables
b. Cumulative distribution functions

c. Survival functions
d. Probability density functions
e. Hazard functions and relationship to Exponential distribution

f. Relationships between failure time random variables in the functions above
g. Greedy algorithms