UniGeniusExam P

Exam P

The Exam P syllabus: three topics and their weights

Exam P has three topics. Univariate random variables is almost half the exam, so that is where most study time belongs.

General Probability23–30% of the exam
Univariate Random Variables44–50% of the exam
Multivariate Random Variables23–30% of the exam

General Probability

  • Sets, Venn diagrams, sample spaces and the axioms of probability
  • Counting with combinations and permutations
  • Independence, mutually exclusive events, addition and multiplication rules
  • Conditional probability, Bayes' theorem and the law of total probability

Univariate Random Variables

  • Discrete distributions: binomial, geometric, hypergeometric, negative binomial, Poisson and uniform
  • Continuous distributions: beta, exponential, gamma, normal and uniform
  • Expected value, moments, mode, median, percentiles, variance and coefficient of variation
  • Insurance payments with deductibles, coinsurance, benefit limits and inflation

Multivariate Random Variables

  • Joint, marginal and conditional distributions for discrete random variables
  • Covariance and correlation
  • Linear combinations of independent random variables, including normal ones
  • The central limit theorem and order statistics

The format

30 multiple-choice questions in 3 hours, each with five choices. A few are unscored pilot questions you cannot tell apart. An unanswered question counts as wrong, so answer every one. A normal distribution table is provided on screen.

Try 3 questions

Question 1

An insurer classifies its drivers as standard (60%), preferred (30%) or high risk (10%). The probability that a driver has an accident during the year is 0.05 for standard, 0.02 for preferred and 0.15 for high risk. A randomly chosen driver has an accident during the year.

Calculate the probability that the driver is high risk.

Question 2

The loss from a theft is exponential with mean $1,000. The policy has a deductible of $250.

Calculate the expected payment by the insurer per loss.

Question 3

An insurer has a portfolio of claims. Each of 100 independent claims has mean 250 and standard deviation 80 dollars.

Using the normal approximation, calculate the probability that the total of the 100 claims exceeds 26,000.

Next step

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SOA's Exam P page, with the current syllabus

Questions people ask

What topics are on Exam P?

Three: General Probability (23 to 30%), Univariate Random Variables (44 to 50%) and Multivariate Random Variables (23 to 30%).

How many questions are on Exam P?

30 multiple-choice questions in 3 hours, about six minutes each.

Is calculus needed for Exam P?

Yes. The syllabus assumes calculus, including series, differentiation and integration. You integrate densities and sum series by hand.