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Losses in year 1 equal <math>X</math> and have an exponential distribution with mean 1,000. Losses in year 2 equal <math>Y</math> and, conditional on <math>X</math>, have an exponential distribution with mean <math>X</math>. Determine the expected value of the maximum annual loss observed in the first two years of coverage. | Losses in year 1 equal <math>X</math> and have an exponential distribution with mean 1,000. Losses in year 2 equal <math>Y</math> and, conditional on <math>X</math>, have an exponential distribution with mean <math>X</math>. Determine the expected value of the maximum annual loss observed in the first two years of coverage. | ||
< | <ul style="list-style-type:upper-alpha"> | ||
<li>735.76</li> | <li>735.76</li> | ||
<li>1,103.64</li> | <li>1,103.64</li> | ||
Revision as of 00:55, 14 April 2023
Losses in year 1 equal [math]X[/math] and have an exponential distribution with mean 1,000. Losses in year 2 equal [math]Y[/math] and, conditional on [math]X[/math], have an exponential distribution with mean [math]X[/math]. Determine the expected value of the maximum annual loss observed in the first two years of coverage.
- 735.76
- 1,103.64
- 1,367.88
- 1,500
- 2,103.64