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Question 1
Which coverage provides protection against damage caused by Unidentified, Uninsured, underinsured motorists?
Correct Answer:
Unidentified, Uninsured, underinsured motorists protection
Explanation:
Unidentified, Uninsured, Underinsured Motorists Protection is designed to cover you when the driver who hits you either has no insurance or not enough to pay for your losses, and also when the other vehicle cannot be identified (a hit-and-run). This coverage fills the gap left by other coverages by paying for your injuries and related losses up to your policy limits if the at-fault driver can’t fully compensate you. It may cover medical expenses, lost wages, and, in some states, non-economic damages like pain and suffering, for you and sometimes your passengers. The other coverages address different situations: third-party bodily injury pays for injuries you cause to others, not your own; medical payments or PIP covers your own medical costs regardless of fault but doesn’t cover the gap when the other driver lacks adequate insurance; collision covers damage to your own car from a crash, not injuries or uninsured motorist issues. So the coverage that specifically targets damage from unidentified, uninsured, or underinsured motorists is Unidentified, Uninsured, Underinsured Motorists Protection.
Question 2
For the second moment of Ax in the continuous case, which formula is correct?
Correct Answer:
Ax second moment = 1 - delta * (second moment annuity)
Explanation:
In continuous-time actuarial math, the discounting uses the force of interest δ, not the nominal rate i. When you look at the second moment of the present value of a unit continuous life annuity, you’re squaring the integral of the discounted payment stream over the lifetime and then taking expectations with respect to survival. Working this out with the double integral and the survival function shows that the effect of discounting enters as a single δ multiplier on the second moment of the corresponding (undiscounted or deterministically structured) payoff. This leads to a neat relation: the second moment of the continuous Ax equals 1 minus δ times the second moment of the (continuous) annuity payoff. The factor is δ (not 2δ), and i or a discrete-second-moment form does not apply in this continuous framework. Therefore the correct formula uses a single δ multiplying the second moment and matches the continuous-discounting setup.
Question 3
In binomial MLE, which constraint must hold for the number of trials m given observed data?
Correct Answer:
m must be at least the largest observed number of successes
Explanation:
In a binomial model, the number of trials m sets the maximum possible number of successes in a single experiment. Since each observed count of successes k must satisfy 0 ≤ k ≤ m, the data can only come from a scenario where m is at least as large as the largest observed count. If m were smaller than that maximum, that observation would have zero probability under the model, which is impossible. So the likelihood is only positive when m ≥ max(k_i) across all observations. That’s why the correct constraint is that m must be at least the largest observed number of successes. The other options don’t fit: m could be larger than the largest observed count, not restricted to be smaller; it isn’t tied to the number of observations; and it need not be a prime number.
Question 4
Put-call parity equation: Which expression holds?
Correct Answer:
c(t) - p(t) = S_t - Ke^{-rt}
Explanation:
Put-call parity shows a fixed relationship between European call and put prices with the same strike and maturity on a non-dividend-paying asset. At expiration, the difference in payoffs between a call and a put with the same strike is (S_T − K). This is because (S_T − K)^+ − (K − S_T)^+ simplifies to S_T − K. If you value that payoff today, its value must equal the difference in option prices: c(t) − p(t) = S_t − K e^{−r(T−t)}. In the notation where the time to maturity is t, this becomes c(t) − p(t) = S_t − K e^{−r t}. So the expression c(t) − p(t) = S_t − K e^{−r t} is the correct relation. The other forms would imply the wrong payoff structure (adding the PV of K or reversing the order), which would not match no-arbitrage pricing.
Question 5
Sum of independent Binomial variables with the same success probability q is distributed as which?
Correct Answer:
Binomial(sum m_i, q)
Explanation:
When you sum independent binomial counts that share the same success probability, you can view all trials together as one big binomial experiment. If each X_i ~ Binomial(m_i, q) and the trials are independent, then the total number of successes X = X_1 + X_2 + ... + X_k behaves like a Binomial with the total number of trials M = sum m_i and the same success probability q. In other words, X ~ Binomial(M, q). This works because each of the M individual trials has probability q of success, and the total number of successes is just counting successes across all these trials. The probability mass function is P(X = k) = C(M, k) q^k (1−q)^{M−k}, with mean E[X] = M q and variance Var[X] = M q (1−q). If the probabilities q differed across X_i, the sum would not be binomial; it would follow a more general Poisson-binomial distribution. The given setup requires the same q, which is why the binomial form with the total number of trials is the correct description.
Question 1
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Prepare with the SOA Fundamentals of Actuarial Mathematics (FAM) Practice Test practice quiz. This question bank includes 10 questions covering expression, formula, binomial, hazard, and fundamentals. Use it to review important concepts, identify knowledge gaps, and build confidence for the related exam, course, or assessment.

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SOA Fundamentals of Actuarial Mathematics (FAM) Practice Test

This practice set contains 10 questions from the matching question bank and focuses on expression, formula, binomial, hazard, and fundamentals. Work through each question carefully, review the provided solutions, and revisit topics that need more study before your next attempt.

This is an independent study resource intended for practice and review; it is not an official examination or an endorsement by any organization named in the title.

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