ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 2
Lesson 2: Parametric Distributions. Lesson 4: Mixtures and Splices.
Problem 1
Claim sizes expressed in deutsche marks follow a lognormal distribution with parameters = 4 and
= 2.5. A euro

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 1
Lesson 1: Basic Probability. Lesson 3: Variance.
Problem 1
You are given the following joint distribution of two random variables X and Y :
(x, y) P r (X, Y ) = (x, y) (x, y) P r (X, Y ) =

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 5
Lesson 9: Other Topics in Severity Coverage Modications.
Lesson 10: Bonuses. Lesson 11: Discrete Distributions.
Problem 1
The loss severity random variable follows an exponential distributi

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 4
Lesson 7: Loss Elimination Ratio. Lesson 8: Risk Measures and Tail Weight.
Problem 1
You are given the following information for a home-owners coverage:
Average
Loss
Ordinary
payment
elimin

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 3
Lesson 5: Policy Limits. Lesson 6: Deductibles.
Problem 1
A sample of 1000 claims contains 500 that are no greater than $4000, 300 that are greater than $4000
but no greater than $6500, and

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 6
Lesson 12: Poisson/Gamma.
Lesson 13: Frequency Distributions: Exposure and Coverage Modications.
Lesson 14: Aggregate Loss Models: Compound Variance.
Problem 1
Claims arrive at a Poisson ra

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 7
Lesson 15: Aggregate Loss Models: Approximating Distribution.
Lesson 16: Aggregate Loss Models: The Recursive Formula.
Problem 1
The number of claims on a policy has a Poisson distribution

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 9
Lesson 19: Review of Mathematical Statistics.
Lesson 20: The Empirical Distribution for Complete Data.
Problem 1
is an estimator for . E[] = 5 and E[2 ] = 32. If = 7, what is the mean squa

ACTS 4304
Instructor: Natalia A. Humphreys
SOLUTION TO HOMEWORK 8
Lesson 17: Aggregate Losses: Aggregate Deductible.
Lesson 18: Aggregate Losses: Miscellaneous Topics.
Problem 1
On an insurance coverage, the number of claims has a negative binomial distri