exercise:38848c0651

A diagnostic test for the presence of a disease has two possible outcomes: 1 for disease present and 0 for disease not present. Let [math]X[/math] denote the disease state (0 or 1) of a patient, and let [math]Y[/math] denote the outcome of the diagnostic test. The joint probability function of [math]X[/math] and [math]Y[/math] is given by:

[[math]] \begin{align*} \operatorname{P}[X = 0, Y = 0] &= 0.800 \\ \operatorname{P}[X = 1, Y = 0] &= 0.050 \\ \operatorname{P}[X = 0, Y = 1] &= 0.025 \\ \operatorname{P}[X = 1, Y = 1] &= 0.125 \\ \end{align*} [[/math]]

Calculate [math]\operatorname{Var}(Y | X = 1) .[/math]

• 0.13
• 0.15
• 0.20
• 0.51
• 0.71

Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.