exercise:48cf40c173: Difference between revisions
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Latest revision as of 19:15, 21 March 2026
Once a fire is reported to a fire insurance company, the company makes an initial estimate, [math]X[/math], of the amount it will pay to the claimant for the fire loss. When the claim is finally settled, the company pays an amount, [math]Y[/math], to the claimant. The company has determined that [math]X[/math] and [math]Y[/math] have the joint density function
[[math]]
f(x,y) = \begin{cases}
\frac{2}{x^2(x-1)}y^{-(2x-1)/(x-1)}, \,\, x \gt1, y \gt 1 \\
0, \, \textrm{Otherwise.}
\end{cases}
[[/math]]
Given that the initial claim estimated by the company is 2, calculate the probability that the final settlement amount is between 1 and 3.
- 1/9
- 2/9
- 1/3
- 2/3
- 8/9
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.