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The annual inflation rate for year 1 has the following discrete distribution: 50% probability of 2% inflation, 30% probability of 1% inflation and 20% probability of no inflation. | |||
Assuming that inflation is independent of loss, determine the probability that losses for year 2 exceed $2,000. | Assuming that inflation is independent of loss, determine the interval containing the probability that losses for year 2 exceed $2,000. | ||
< | <ul class="mw-excansopts"> | ||
<li>[0.035, 0.04]</li> | <li>[0.035, 0.04]</li> | ||
<li>[0.045, 0.05]</li> | <li>[0.045, 0.05]</li> | ||
| Line 19: | Line 19: | ||
<li>[0.07, 0.08]</li> | <li>[0.07, 0.08]</li> | ||
<li>[0.09, 0.1]</li> | <li>[0.09, 0.1]</li> | ||
</ | </ul> | ||
Latest revision as of 21:05, 31 March 2025
Losses for year 1 equal
[[math]]\frac{1500(1-X^{1/3})}{1 + X^{1/3}}[[/math]]
with [math]X[/math] a non-negative random variable bounded by 1 with cumulative distribution function
[[math]]
F(u) = 1-x^2.
[[/math]]
The annual inflation rate for year 1 has the following discrete distribution: 50% probability of 2% inflation, 30% probability of 1% inflation and 20% probability of no inflation.
Assuming that inflation is independent of loss, determine the interval containing the probability that losses for year 2 exceed $2,000.
- [0.035, 0.04]
- [0.045, 0.05]
- [0.055, 0.06]
- [0.07, 0.08]
- [0.09, 0.1]