You are given:

1. The number of claims has a Poisson distribution.
2. Claim sizes have a Pareto distribution with parameters [math]\theta = 0.5 [/math] and [math]\alpha = 6[/math]
3. The number of claims and claim sizes are independent.
4. The observed average total payment should be within 2% of the expected average total payment 90% of the time.

Calculate the expected number of claims needed for full credibility.

• Less than 7,000
• At least 7,000, but less than 10,000
• At least 10,000, but less than 13,000
• At least 13,000, but less than 16,000
• At least 16,000

You are given the following information about a commercial auto liability book of business:

1. Each insured’s claim count has a Poisson distribution with mean [math]\lambda [/math] , where [math]\lambda [/math] has a gamma distribution with [math]\alpha = 1.5[/math] and [math]\theta = 0.2 [/math].
2. Individual claim size amounts are independent and exponentially distributed with mean 5000.
3. The full credibility standard is for aggregate losses to be within 5% of the expected with probability 0.90.

Calculate the expected number of claims required for full credibility using limited fluctuated credibility.

• 2165
• 2381
• 3514
• 7216
• 7938

You are given the following information about a general liability book of business comprised of 2500 insureds:

1. [math]X_i = \sum_{j=1}^{N_i}Y_{ij} [/math] is a random variable representing the annual loss of the i^th insured.
2. [math]N_1,N_2,\ldots,N_{2500}[/math] are independent and identically distributed random variables following a negative binomial distribution with parameters [math]r = 2[/math] and [math]\beta = 0.2[/math].
3. [math]Y_{i1},Y_{i2},\ldots,Y_{iN}[/math] are independent and identically distributed random variables following a Pareto distribution with [math]\alpha = 3[/math] and [math]\theta = 1000 [/math].
4. The full credibility standard is to be within 5% of the expected aggregate losses 90% of the time.

Calculate the partial credibility of the annual loss experience for this book of business using limited fluctuation credibility theory.

• 0.34
• 0.42
• 0.47
• 0.50
• 0.53

You are given:

1. The number of claims has probability function:

1. The actual number of claims must be within 1% of the expected number of claims with probability 0.95.
2. The expected number of claims for full credibility is 34,574.

Calculate q.

• 0.05
• 0.10
• 0.20
• 0.40
• 0.80

A company has determined that the limited fluctuation full credibility standard is 2000 claims if:

1. The total number of claims is to be within 3% of the true value with probability p.
2. The number of claims follows a Poisson distribution.

The standard is changed so that the total cost of claims is to be within 5% of the true value with probability p, where claim severity has probability density function:

Calculate the expected number of claims necessary to obtain full credibility under the new standard using limited fluctuation credibility.

• 720
• 960
• 2160
• 2667
• 2880

You are given:

1. The number of claims follows a Poisson distribution.
2. The number of claims and claim severity are independent.
3. The severity distribution is:

Calculate the expected number of claims needed so the total cost of claims is within 5% of the expected with probability 0.90.

• 511
• 726
• 1083
• 2044
• 3126