Question 1200583
**1. Define Net Revenue**

* **Net Revenue = Premium Revenue - Expected Claim Cost**

**2. Calculate Premium Revenue**

* Premium Revenue = Premium per policy * Probability of no claim + Premium per policy * Probability of claim
* Premium Revenue = $7 * (1 - 0.43) + $7 * 0.43 = $7 

**3. Calculate Expected Claim Cost**

* **Expected Claim Cost = Probability of claim * Expected claim amount**

* **Find Expected Claim Amount:**

   * Expected Claim Amount = ∫(x * f(x)) dx 
      where f(x) is the probability density function of the claim amount 
      and the integral is taken over the range of possible claim amounts (x ≥ 1)

   * Expected Claim Amount = ∫(x * (1.2/x^2.2)) dx from 1 to infinity
   * Expected Claim Amount = 1.2 ∫(x^(-1.2)) dx from 1 to infinity

   * To solve this improper integral, we need to find the limit as the upper bound approaches infinity:

      * Expected Claim Amount = 1.2 * lim (b→∞) [(-1/0.2) * x^(-0.2)] from 1 to b
      * Expected Claim Amount = -6 * lim (b→∞) [b^(-0.2) - 1^(-0.2)]
      * Expected Claim Amount = -6 * (0 - 1) = 6

* **Expected Claim Cost = 0.43 * 6 = 2.58**

**4. Calculate Net Revenue**

* Net Revenue = $7 - $2.58 = $4.42

**Therefore, the expected value of the net revenue to the company is $4.42.**