Exam P practice exam and study guide

Exam P practice problems: Continuous distributions

10 problems · Untimed · Worked solution after each answer

Densities and CDFs, the uniform, exponential, gamma, beta and normal distributions, percentiles, the median and mode, and conditional probabilities. This drill covers topic 2 of the Exam P syllabus, Univariate Random Variables (44–50% of the exam).

  • 2a Random variables, densities and CDFs
  • 2b Conditional probabilities
  • 2c Expected values, moments, mode, median and percentiles
  • 2d Variance, standard deviation and coefficient of variation

Before you start

  • Every problem has five options, A to E, and one correct answer, as on the real exam. Every value you need is in the problem, so you can work it with an approved calculator; the worked solution shows each step and names the mistake behind the most tempting wrong answer.
  • Check each answer to see the explanation before moving on. Checked answers cannot be changed.

Study guide: Continuous distributions

  • A density must integrate to 1, which fixes an unknown constant; the CDF is the integral of the density from the lower end.
  • The exponential is memoryless: P(T > s + t | T > s) = P(T > t), and its median is θ·ln 2, below its mean θ.
  • A percentile solves F(x) = p; the mode maximizes the density.
  • For a normal variable, standardize with z = (x − μ)/σ and round z to two decimals for the table SOA supplies.

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Original practice problems written to the published SOA syllabus; not SOA sample questions. Independent preparation, not affiliated with or endorsed by the Society of Actuaries (SOA).