⧼exchistory⧽
To view all exercises, please subscribe to guide
23 exercise(s) shown, 46 hidden
ABy Admin
May 14'23
The repair costs for boats in a marina have the following characteristics:
| Boat type | Number of boats | Probability that repair is needed | Mean of repair cost given a repair | Variance of repair cost given a repair |
| Power boats | 100 | 0.3 | 300 | 10,000 |
| Sailboats | 300 | 0.1 | 1000 | 400,000 |
| Luxury yachts | 50 | 0.6 | 5000 | 2,000,000 |
At most one repair is required per boat each year. Repair incidence and cost are mutually independent. The marina budgets an amount, [math]Y[/math], equal to the aggregate mean repair costs plus the standard deviation of the aggregate repair costs.
Calculate [math]Y[/math].
- 200,000
- 210,000
- 220,000
- 230,000
- 240,000
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.
ABy Admin
May 14'23
You are given:
- The number of claims follows a negative binomial distribution with parameters [math]r[/math] and [math]\beta = 3 [/math].
- Claim severity has the following distribution:
| Claim Size | Probability |
| 1 | 0.4 |
| 10 | 0.4 |
| 100 | 0.2 |
Calculate the expected number of claims needed for aggregate losses to be within 10% of expected aggregate losses with 95% probability.
- Less than 1200
- At least 1200, but less than 1600
- At least 1600, but less than 2000
- At least 2000, but less than 2400
- At least 2400
Copyright 2023. The Society of Actuaries, Schaumburg, Illinois. Reproduced with permission.