The claim frequency, [math]N[/math], for a policy has a binomial distribution with the following properties:

Determine [math]\operatorname{P}[N=4][/math].

1. 0.0301
2. 0.0329
3. 0.0412
4. 0.0465
5. 0.0493

A large portfolio of travel insurance policies contains policies with three different deductible levels: 50% have a deductible of $200, 25% have a deductible of $400 and 25% have a deductible of $600. Ten policies are randomly chosen from the portfolio of policies two of which have a deductible of $600. Determine the probability that more than six of the policies chosen have a deductible of $400.

1. 0
2. 0.0351
3. 0.1951
4. 0.225
5. 0.2351

The probability function for the claim frequency is given below

What is the probability that the claim frequency will lie within one standard deviation of the mean of the claim frequency distribution?

1. 0.1631
2. 0.4694
3. 0.6231
4. 0.6689
5. 0.8011

An insurer sells an annual policy with a claim frequency with the following distribution:

The parameter [math]q[/math] is unknown but your prior beliefs indicate that it has the following density function on [0,1]:

Determine the expected annual claim frequency.

1. 0.6
2. 2.3
3. 2.4
4. 3.25
5. 4

The claim frequency [math]N[/math] has the following properties:

• The claim frequency has a geometric distribution
• The probability that [math]N=1[/math] given that [math]N\gt0[/math] equals 0.3

Determine the variance of the claim frequency given that [math]N\gt0[/math].

1. 0.4671
2. 1.19
3. 3.1477
4. 3.477
5. 7.77

The following is known about the monthly claim frequency:

• The monthly claim frequency has a geometric distribution
• The probability that there are 4 claims in a month is half the probability that there are 2 claims in a month
• Monthly claim frequencies are independent

Determine the variance of the annual claim frequency.

1. 3.41
2. 40.97
3. 38.95
4. 42.15
5. 69.94

A hospital receives 1/5 of its flu vaccine shipments from Company X and the remainder of its shipments from other companies. Each shipment contains a very large number of vaccine vials.

For Company X’s shipments, 10% of the vials are ineffective. For every other company, 2% of the vials are ineffective.

The hospital tests 30 randomly selected vials from a shipment and finds that one vial is ineffective.

Calculate the probability that this shipment came from Company X.

• 0.10
• 0.14
• 0.37
• 0.63
• 0.86

An actuary has discovered that policyholders are three times as likely to file two claims as to file four claims. The number of claims filed has a Poisson distribution.

Calculate the variance of the number of claims filed.

• [math]\frac{1}{\sqrt{3}}[/math]
• 1
• [math]\sqrt{2}[/math]
• 2
• 4

A company establishes a fund of 120 from which it wants to pay an amount, C, to any of its 20 employees who achieve a high performance level during the coming year. Each employee has a 2% chance of achieving a high performance level during the coming year. The events of different employees achieving a high performance level during the coming year are mutually independent.

Calculate the maximum value of C for which the probability is less than 1% that the fund will be inadequate to cover all payments for high performance.

• 24
• 30
• 40
• 60
• 120

A large pool of adults earning their first driver’s license includes 50% low-risk drivers, 30% moderate-risk drivers, and 20% high-risk drivers. Because these drivers have no prior driving record, an insurance company considers each driver to be randomly selected from the pool.

This month, the insurance company writes four new policies for adults earning their first driver’s license.

Calculate the probability that these four will contain at least two more high-risk drivers than low-risk drivers.

• 0.006
• 0.012
• 0.018
• 0.049
• 0.073