Exam P practice problems: Joint distributions, covariance and correlation

10 problems · Untimed · Worked solution after each answer

Joint, marginal and conditional probability functions of discrete variables, conditional means and variances, covariance and correlation. This drill covers topic 3 of the Exam P syllabus, Multivariate Random Variables (23–30% of the exam).

3a Joint probability functions and CDFs
3b Conditional and marginal distributions
3c Joint, conditional and marginal moments
3d Conditional and marginal variance
3e Covariance and correlation

Line drawing of a navy die and a pale blue die on a checkerboard

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: Joint distributions, covariance and correlation

Marginals are row and column sums of the joint table; a conditional distribution is one row or column divided by its total.
Cov(X, Y) = E[XY] − E[X]E[Y], and ρ = Cov(X, Y) / (σ_X σ_Y).
The law of total variance: Var(X) = E[Var(X | Y)] + Var(E[X | Y]).
Zero covariance does not mean independence; independence needs every joint probability to factor.

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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).