Question 1
A model predicts claim severity, in thousands. At a particular predictor value , the estimate has bias −0.6 and variance 0.45 over repeated training sets, and the irreducible error has variance 1.20.
Calculate the expected test MSE at .
Exam SRM sample questions, with full solutions
Ten questions in the exam's style, weighted like the syllabus: one on statistical learning, four on linear models, two on decision trees, and one or two each on time series and unsupervised learning. Pick an answer to check it.
Try 10 questions
Question 2
A commercial property insurer models fire losses, in dollars, using floor area in thousands of square feet (area) and whether the building has sprinklers (sprinkler, with levels No and Yes). The ordinary least squares output of lm(log(loss) ~ area + sprinkler) is below.
| | Estimate | Std. Error | t value | p-value | |---|---|---|---|---| | (Intercept) | 7.9623 | 0.1038 | 76.738 | < 2e-16 | | area | 0.0316 | 0.0040 | 7.837 | 1.28e-10 | | sprinklerYes | −0.1404 | 0.0910 | −1.544 | 0.1281 |Residual standard error: 0.351 on 57 degrees of freedom. Multiple R-squared: 0.5211, adjusted R-squared: 0.5043.
The predicted loss is e raised to the fitted value of log(loss). Calculate the percentage reduction in predicted loss for a building with sprinklers compared with one of the same area without sprinklers.
Question 3
An actuary fits a linear model to 40 auto claims. The response is claim severity, in hundreds of dollars; the predictors are driver age (age, years), vehicle value (value, thousands of dollars) and annual mileage (mileage, thousands of miles). For a driver aged 60 with a vehicle worth $55,000 and 22,000 miles a year, predict(fit, newdata, se.fit = TRUE) gives the output below.
| fit | se.fit | df | residual.scale |
|---|---|---|---|
| 45.8075 | 1.6760 | 36 | 4.1862 |
You are given t(0.975, 36) = 2.0281.
Calculate the upper limit of the 95% prediction interval for the severity of a single new claim from such a driver.
Question 4
An insurer fits a logistic regression to 500 policies at renewal. The response lapse is 1 if the policy lapsed and 0 otherwise. The predictors are age, the policyholder's age in years; incr, the premium rate increase at renewal in percentage points; and channel, the sales channel (Agent, Broker or Direct, with Agent as the base level). The output is below.
| | Estimate | Std. Error | z value | p-value | |---|---|---|---|---| | (Intercept) | −0.7568 | 0.4132 | −1.832 | 0.067 | | age | −0.0404 | 0.0076 | −5.312 | 1.08e-07 | | incr | 0.1579 | 0.0196 | 8.059 | 7.71e-16 | | channelBroker | 0.4785 | 0.2600 | 1.840 | 0.0657 | | channelDirect | 0.8937 | 0.2626 | 3.403 | 0.000666 |Calculate the odds ratio of lapse for a Direct policyholder relative to an Agent policyholder with the same age and rate increase.
Question 5
A least squares model for claim severity with d = 3 predictors is fitted to n = 40 policies and has RSS = 83.27. The error variance estimated from the model with all 6 candidate predictors is .
Calculate AIC for the three-predictor model.
How to use them
- Give each question six minutes, the real exam's pace.
- Read the R output before you compute: which row, which column, and on what scale.
- Read the solution even when you are right: the shortest route matters on the day.
More practice
These ten are written for this course, to the January 2027 syllabus. SOA publishes its own sample questions with solutions as well. The free 90-minute diagnostic gives 15 more, marked by topic, and the course has two full 35-question practice exams.
Next step
The same page for Exam P · The same page for Exam FM · The same page for Exam FAM
Questions people ask
Where can I find Exam SRM practice questions?
Ten are on this page with full solutions. SOA publishes its own sample questions, and the free diagnostic here gives 15 more, marked by topic.
How many questions are on Exam SRM?
35 multiple-choice questions in 3.5 hours, each with five answer choices. A few are unscored pilot questions you cannot tell apart.
Are past Exam SRM exams released?
No. SOA does not release past Exams P, FM, FAM or SRM, so sample questions are the closest practice to the real paper.
Do I need to know R for Exam SRM?
No. SOA's syllabus says the ability to solve problems in R is not assumed, but questions may show R output for you to interpret. Many questions here do the same.