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MAS-I Probability Models

The MAS-I probability-models domain covers stochastic processes and survival models: Poisson processes, limited expected value, hazard rates, joint life calculations, simple whole life, and annuity work.

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MAS-I probability models

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MAS-I Statistics

Official Source Map

CAS Exam MAS-I

CAS exam page and content outline are mapped for domain weights, item types, cognitive levels, table conventions, and reading groups.

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Last verified 2026-05-141 official source filesNo raw exam or textbook text published

Exam facts

What the official PDFs establish

Appointment length: 4.5-hour appointment with a 4-hour exam duration.
Scheduled break: The appointment includes a scheduled 15-minute break plus tutorial/confidentiality/survey time.
Item types: Question formats include multiple choice, multiple selection, point and click, fill in the blank, and matching.

Weights

Topic and domain coverage

Topic	Weight	Source
Probability Models	20-30%	Source: MAS-I Content Outline 2025, p. 2
Statistics	20-30%	Source: MAS-I Content Outline 2025, p. 3
Extended Linear Models	45-55%	Source: MAS-I Content Outline 2025, p. 5
Cognitive level: Remember	5-10%	Source: MAS-I Content Outline 2025, p. 1
Cognitive level: Understand and Apply	55-60%	Source: MAS-I Content Outline 2025, p. 1
Cognitive level: Analyze and Evaluate	35-40%	Source: MAS-I Content Outline 2025, p. 1

Readings

Chapter and reading intelligence

Official readings
The outline lists readings from Daniel, Dobson and Barnett, Hogg/McKean/Craig, James et al., Larsen, Ross, Struppeck, and Tse.
Source: MAS-I Content Outline 2025, p. 7
Extended linear models
This is the largest content domain and should drive the first MAS-I concept cluster.
Source: MAS-I Content Outline 2025, p. 5

Materials

Official files used by the map

CAS content outlinecontent-outline
Primary source for domain weights, item types, and readings.
Source: MAS-I Content Outline 2025

Source note: some study materials are private references. ActuaryPath links official sources and uses original explanations instead of republishing paid or copyrighted materials.

Quick Answer

The official MAS-I outline gives probability models a 20-30% weight and names stochastic processes, Poisson processes, limited expected value, survival models, hazard rates, joint life calculations, and simple whole life or annuity problems.

This domain is where P-style probability becomes actuarial. The exam is less interested in isolated distributions than in what a process or survival model says about claims, waiting times, lives, and payments.

Poisson Process Core

Poisson process questions usually ask about counts in time intervals, waiting times, independent increments, or conditional timing. The clean setup is to define the rate, the interval length, and the event being counted before calculating.

A common MAS-I mistake is to use the Poisson count formula when the question is actually about waiting time, or to use exponential waiting time when the question asks for the nth arrival.

Poisson count

P\{N(t)=k\}=e^{-\lambda t}\frac{(\lambda t)^k}{k!}

Waiting time to the nth event

T_n\sim \operatorname{Gamma}(n,\lambda)

Independent increments

Counts over disjoint time intervals are independent in a Poisson process.

The distribution of the count over an interval depends on the interval length, not on where the interval sits on the timeline, when the process is homogeneous.

Limited Expected Value

Limited expected value converts a loss distribution into an expected capped amount. It is a natural actuarial bridge from severity distributions into deductibles, limits, and aggregate models.

For MAS-I, know the notation, the survival-function identity, and the connection to stop-loss payments. The exam can test the calculation directly or hide it inside a claim-size model.

Limited expected value

E[X\wedge u]=\int_0^u S_X(x)\,dx

Stop-loss complement

E[(X-u)_+]=E[X]-E[X\wedge u]

Survival And Hazard

Survival-model questions ask for probabilities or expected values tied to a lifetime or duration variable. Hazard-rate questions ask how the instantaneous failure rate connects to the survival curve.

The most useful exam habit is to keep density, distribution, survival, and hazard separate. The survival function is probability beyond t. The hazard rate is a local rate conditional on survival to t.

Hazard rate

h(t)=\frac{f(t)}{S(t)}

Survival from hazard

S(t)=\exp\left(-\int_0^t h(u)\,du\right)

Joint Life And Simple Benefits

The MAS-I outline includes joint life calculations and simple whole life or annuity problems. This is not a full ALTAM-style life-contingencies exam, but candidates should know enough to translate survival probabilities into simple benefit and annuity calculations.

For joint lives, name whether the payment depends on the first death, last survivor, or another condition. That statement usually determines whether the lifetime is a minimum, maximum, or conditional event.

Original Practice Drill

Claims arrive according to a Poisson process with rate 0.8 per month. Calculate the probability of exactly three claims in two months, then calculate the probability that the waiting time to the second claim is greater than two months.

A complete MAS-I answer identifies the first part as a Poisson count and the second as an arrival-time event. If both parts are solved with the same formula, the setup is probably wrong.