Insurance claims are made according to a Poisson process \{N(t), t \ge 0\} with rate \lambda = 1 . Calculate E[N(1) \cdot N(2)] .

At least 1.5, but less than 2.5

At least 3.5, but less than 4.5

SOA vs CAS Exams Quiz: 10-Question Actuarial Sampler (2026)

How this sampler works. Pick an answer, reveal the solution, and read the note on which exam it came from. It measures the style of each track, not your aptitude. The real SOA-versus-CAS decision is about the industry you want to work in, so treat the per-track score at the end as a taste, not a verdict.

The 10-question sampler

0 of 10 answers revealed

Joint prelims: Exam P and Exam FM

Both societies require these two, and they are the same exams for either path. Most candidates start here before deciding.

Q1 · Exam P (SOA / CAS) Easy

N ~ Poisson(3). Find E[N²].

Solution

E is correct.

For a Poisson distribution,

E [N^{2}] = Var (N) + (E [N])^{2}

. Since

Var (N) = 3

and

E [N] = 3

E [N^{2}] = Var (N) + (E [N])^{2} = 3 + 9 = 12.

FROM EXAM P · JOINT PRELIM

Exam P is the probability gateway that both the SOA and the CAS require, and questions like this one, pure distribution theory with a clean numeric answer, are its signature. You get E[N squared] straight from the variance-plus-mean-squared identity. Watch for the same Poisson turning up on the CAS side, where MAS-I stretches it into a Poisson process over time.

More about Exam P →

Q2 · Exam FM (SOA / CAS) Easy

Calculate the present value of $50,000 due in 12 years at an effective annual interest rate of 3%.

Solution

C is correct.

The present value is:

P V = F V \cdot v^{n} = \frac{F V}{( 1 + i ) ^{n}} = \frac{50 , 000}{( 1.03 ) ^{12}}

Compute

(1.03)^{12}

by repeated squaring:

(1.03)^{2} = 1.0609

(1.03)^{4} = (1.0609)^{2} = 1.12550881

(1.03)^{8} = (1.12550881)^{2} = 1.26677008

(1.03)^{12} = (1.03)^{8} \times (1.03)^{4} = 1.26677008 \times 1.12550881 = 1.42576089

P V = \frac{50 , 000}{1.42576089} = 35, 069

The present value is $35,069.

FROM EXAM FM · JOINT PRELIM

Exam FM is the second joint prelim, and it is almost entirely calculator work: discounting cash flows, valuing annuities, and pricing bonds. Here you discount a single future amount back twelve years at 3 percent. If Exam P rewards knowing the theory, FM rewards being fast and exact with the time value of money.

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SOA track: FAM, SRM, ALTAM, ASTAM

The Society of Actuaries path, weighted toward life, health, and pension work, with loss models and life contingencies.

Q3 · Exam FAM (SOA) Medium

Which of the following statements about TVaR is FALSE?

Solution

B is correct.

TVaR_{0} = E [X]

, while

VaR_{0}

is the minimum possible value (often 0 for loss distributions). Since

E [X]

generally does not equal the minimum, the statement that TVaR at level

p = 0

equals VaR at level

p = 0

is false.

FROM EXAM FAM · SOA TRACK

Exam FAM is where the SOA track begins in earnest, blending short-term loss models with an introduction to life contingencies. This question tests tail value at risk, a coherent risk measure at the center of the loss-modeling half. The CAS track leans harder into applied statistics than into risk measures like this one.

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Q4 · Exam SRM (SOA) Easy

In a GLM, Pearson residuals are defined as:

Solution

D is correct.

The Pearson residual for observation

i

in a GLM is defined as:

r_{P, i} = \frac{y _{i} - μ ^ _{i}}{V ( μ ^ _{i} )}

where

V (μ^_{i})

is the variance function of the assumed distribution evaluated at the fitted mean. This standardizes the raw residual by the expected standard deviation under the model.

FROM EXAM SRM · SOA TRACK

Exam SRM is the SOA statistics exam, heavy on regression and generalized linear models. Pearson residuals standardize a raw residual by the model variance function. Keep this one in mind for the MAS-I question further down: the CAS statistics content overlaps SRM so closely that a candidate who studied one often finds the other familiar.

More about Exam SRM →

Q5 · Exam ALTAM (SOA) Easy

Under which of the following conditions does a universal life policy lapse?

Solution

B is correct.

A universal life policy lapses when the account value is reduced to zero or below after charges are applied and the policyholder fails to make a sufficient premium payment within the grace period (typically 61 days) to restore a positive account value. This is the defining feature of UL's flexible premium structure: the policy persists only as long as the account value is sufficient to cover ongoing COI and expense charges.

FROM EXAM ALTAM · SOA TRACK

Exam ALTAM is an advanced SOA-only exam built around long-term insurance and pensions, with no CAS counterpart. A universal life policy lapses when its account value runs to zero and a grace-period premium does not restore it. This product-mechanics flavor, life insurance and annuities, is what most separates the SOA path from the property-and-casualty CAS path.

More about Exam ALTAM →

Q6 · Exam ASTAM (SOA) Easy

In the Bühlmann credibility model, the credibility factor

Z

for

n

years of experience is:

Solution

D is correct.

In the Bühlmann model, the credibility factor is

Z = n / (n + k)

where the Bühlmann parameter

k = v / a

v = E [σ^{2} (Θ)]

is the expected value of the process variance, and

a = Var [μ (Θ)]

is the variance of the hypothetical means. Substituting

k

gives

Z = n / (n + v / a)

, as stated.

FROM EXAM ASTAM · SOA TRACK

Exam ASTAM is the advanced short-term SOA exam, covering severity and aggregate models, reserving, and credibility. The Buhlmann credibility factor weights recent experience against a prior mean. Credibility shows up on the CAS side too, inside MAS-II, which is one of the places the two tracks quietly converge.

More about Exam ASTAM →

CAS track: MAS-I and MAS-II

The Casualty Actuarial Society path, weighted toward property and casualty insurance and applied statistics.

Q7 · MAS-I (CAS) Easy

Insurance claims are made according to a Poisson process

{N (t), t \geq 0}

with rate

λ = 1

.

Calculate

E [N (1) \cdot N (2)]

Solution

D is correct.

We need

E [N (1) \cdot N (2)]

. Write

N (2) = N (1) + [N (2) - N (1)]

. By independent increments,

N (1)

and

N (2) - N (1)

are independent.

E [N (1) \cdot N (2)] = E [N (1) (N (1) + (N (2) - N (1)))]

= E [N (1)^{2}] + E [N (1)] E [N (2) - N (1)]

For Poisson with

λ = 1

E [N (1)] = 1

Var (N (1)) = 1

, so

E [N (1)^{2}] = 1 + 1 = 2

. Also

E [N (2) - N (1)] = 1

E [N (1) \cdot N (2)] = 2 + 1 \cdot 1 = 3

FROM MAS-I · CAS TRACK

MAS-I is the first Modern Actuarial Statistics exam on the CAS track, and its probability-models section extends the single-variable Poisson from Exam P into a Poisson process over time. Notice the answer choices are ranges rather than exact values. That interval format is standard on CAS multiple choice and is something a first-time CAS candidate should get used to.

More about MAS-I →

Q8 · MAS-I (CAS) Easy

Which of the following statements is TRUE regarding the use of an offset variable in a generalized linear model?

Solution

C is correct. An offset is a known quantity that enters the linear predictor with a coefficient fixed at 1 (rather than being estimated from the data). For a Poisson GLM with log link, the linear predictor is

η = β_{0} + β_{1} x_{1} + \dots + lo g (exposure)

, so the predicted count scales proportionally with exposure. This is the standard mechanism for handling unequal time-at-risk or other normalizing quantities in count and severity models.

FROM MAS-I · CAS TRACK

Extended linear models make up close to half of MAS-I, and generalized linear models are the core tool for insurance ratemaking. An offset enters the linear predictor with its coefficient fixed at 1, the standard way to handle unequal exposure. Compare this with the SRM question above: the GLM material on the CAS side is nearly the same as on the SOA statistics exam.

More about MAS-I →

Q9 · MAS-II (CAS) Easy

Which of the following is NOT a standard assumption of a linear mixed model with random intercepts?

Solution

D is correct. The standard assumptions of a Gaussian linear mixed model with random intercepts are: (1) the random effects satisfy

u_{j} \sim N (0, σ_{u}^{2})

; (2) the residuals satisfy

ϵ_{ij} \sim N (0, σ_{e}^{2})

with constant variance; (3) the random effects are independent of the residuals; and (4) observations within a cluster are conditionally independent given the random effects. Orthogonality of the fixed-effect design columns is never required. Correlated predictors simply affect interpretation and standard errors. They do not invalidate the model.

FROM MAS-II · CAS TRACK

MAS-II is the second CAS statistics exam, and linear mixed models are one of its pillars. The question turns on which assumptions a random-intercept model actually requires, and orthogonal predictors are never one of them. This is graduate-level applied statistics, well beyond anything on the joint prelims.

More about MAS-II →

Q10 · MAS-II (CAS) Easy

Which of the following best distinguishes K-means clustering from agglomerative hierarchical clustering?

Solution

E is correct. K-means partitions observations into a pre-specified number of disjoint clusters by iteratively reassigning observations and updating centroids; the analyst must choose K before running the algorithm. Agglomerative hierarchical clustering instead builds a tree of nested partitions by successively merging the closest groups, and any desired number of clusters can be obtained after the fact by cutting the dendrogram at an appropriate height. This is the defining structural contrast between the two methods.

FROM MAS-II · CAS TRACK

Statistical learning is the largest topic on MAS-II, spanning clustering, trees, and regularization. The defining contrast here is that K-means needs its cluster count chosen in advance while hierarchical clustering yields a full dendrogram. If this material draws you in more than life-contingency notation did, that is a genuine signal the CAS path may suit you.

More about MAS-II →

Reveal all 10 answers to unlock your per-track breakdown.

What this quiz can and cannot tell you

Ten questions is a taste, not a diagnosis. Two to four questions per track is enough to feel the style, not enough to rank your ability. And there is a deeper reason the score is only directional: the two tracks overlap more than they look. MAS-I reuses much of the probability from Exam P and much of the statistics from Exam SRM, and MAS-II overlaps SRM heavily as well. So scoring well on the CAS questions mostly means you are good at probability and statistics, which helps on both tracks.

The decision that actually matters is not on this page. It is which industry you want to spend a career in. The SOA credentials (ASA, FSA) lead to life insurance, health insurance, and retirement and pension work. The CAS credentials (ACAS, FCAS) lead to property and casualty insurance: auto, home, workers' compensation, reinsurance. Pick the work first; the exams follow from there. And because Exams P and FM count for both, you can start studying today without having decided.

SOA vs CAS at a glance

	SOA	CAS
Sponsoring body	Society of Actuaries	Casualty Actuarial Society
Industry focus	Life, health, retirement and pensions	Property and casualty insurance
Shared prelims	Exam P and Exam FM (jointly administered)
Path-specific exams	FAM, SRM, ALTAM, ASTAM, then FSA modules	MAS-I, MAS-II, then CAS Exams 5 to 9
Question style	Multiple choice, plus written answer on ALTAM and ASTAM	Multiple choice with interval-range answers, plus written answer on later exams
Time to fellowship	Typically 6 to 10 years	Typically 6 to 10 years

For the full career comparison, salaries, timelines, and how to choose, read SOA vs CAS: Life/Health vs P&C Actuarial Paths.

Frequently Asked Questions

Do the SOA and CAS share any exams?

Yes. Exam P (Probability) and Exam FM (Financial Mathematics) are jointly administered by the Society of Actuaries and the Casualty Actuarial Society. The same sitting counts for either society, so you can pass both before you commit to a track.

Which track is harder, SOA or CAS?

Neither is objectively harder; both take most candidates six to ten years and both have low pass rates per sitting. The difference is emphasis. The CAS path is statistics-forward (regression, GLMs, statistical learning), while the SOA path carries more life-contingency and insurance-product material. Which one feels harder depends on your background.

Can this quiz tell me whether to choose SOA or CAS?

No. Ten questions samples the style of each track, not your aptitude or your fit. The per-track score is a taste, not a diagnosis. The real decision is which industry you want to work in: life, health, and pensions on the SOA side, or property and casualty insurance on the CAS side.

Do CAS exams use a different question format?

On the multiple-choice exams, CAS often gives answer choices as ranges (for example, "at least 2.5, but less than 3.5") rather than a single exact value, which nudges you to bound your answer. Later CAS exams move to written-answer questions. The SOA advanced exams (ALTAM, ASTAM) also mix in written-answer sections.

Where should I start if I want to be an actuary?

Start with Exam P or Exam FM. They count for both societies, so you keep both doors open while you decide. FreeFellow has a free diagnostic and the full question bank for each, with worked solutions and no signup to start.

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SOA vs CAS: Answer 10 Questions From Both Actuarial Tracks

The 10-question sampler

Joint prelims: Exam P and Exam FM

SOA track: FAM, SRM, ALTAM, ASTAM

CAS track: MAS-I and MAS-II

Your track breakdown

What this quiz can and cannot tell you

SOA vs CAS at a glance

Frequently Asked Questions

Practice any of these free