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]