SOA Exam P Sample Question 284

Study guide: Exam P-1

An employer provides disability benefits to its employees for work-related and other injuries. The random variables $X$ and $Y$ denote the employer's annual expenditures for work-related and other injuries, respectively. An actuarial study reveals the following information about $X$ and $Y$ :

(i) The density of $X$ is $f(x) = \frac{1}{20\sqrt{5}} e^{\frac{-x}{20\sqrt{5}}}$ , for $x > 0$ .
(ii) $\text{Var}(Y) = 12{,}500$ .
(iii) The correlation between $X$ and $Y$ is 0.20.

Calculate the variance of the employer's total expenditures for work-related and other injuries.

A) 12,500
B) 13,500
C) 15,500
D) 16,500
E) 18,972

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Concepts tested

Covariance
Variance
Correlation Coefficient
Exponential Distribution

SOA Exam P Sample Question 284

Concepts tested

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