Question

3. Suppose a whole-life policy from the insurance company has a 55% chance of lapsing in its first year.

1. Describe the sample space for the variable L if L denotes the single event of the policy lapsing (0.5 point)

2. What type of distribution would this be? (0.5 point)____________________________________

3. Assign probabilities to each value of L (0.5 point)

4. Calculate the expected value and the variance of L (0.5 point)

For Reference:

1. An insurance company is concerned about the persistency (length of time a policy remains in-force and doesn’t lapse) of its whole-life policies. Suppose the persistency of the company’s whole-life policies is normally distributed with a mean of 13 years and a standard deviation of 4 years.

1. What is the probability that the persistency of a whole-life policy will be less than 10 years? (1 point)

2. If the insurance company wants no more than 5% of its whole-life policies to have a persistency of less than 8 years, what does its mean persistency need to be? (Assume the same standard deviation) (1 point)

2. Jenni is an insurance agent for the company listed in question 1. The number of whole-life policies she has written (sold) that lapse is Poisson distributed with a mean of 12 policies per year.

1. What is the probability only 9 of Jenni’s whole-life policies will lapse in a given year? (1 point)

2. What is the probability 16 of Jenni’s whole-life policies will lapse in a given year? (1 point)

Answer 1