The practice problems in this post focus on counting distributions that belong to the (a,b,0) class, reinforcing the concepts discussed in this blog post in a companion blog.
The (a,b,1) class is a generalization of (a,b,0) class. It is discussed here. A practice problem set on the (a,b,1) class is found here.
Notation: for where is the counting distribution being focused on.
Practice Problem 11A 
Suppose that claim frequency follows a negative binomial distribution with parameters and . The following is the probability function.
Evaluate the negative binomial distribution in two ways.

Practice Problem 11B 
Suppose that follows a distribution in the (a,b,0) class. You are given that Evaluate the probability that is at least 1. 
Practice Problem 11C 
The following information is given about a distribution from the (a,b,0) class. What is the form of the distribution? Evaluate . 
Practice Problem 11D 
For a distribution from the (a,b,0) class, the following information is given. Determine the variance of this distribution. 
Practice Problem 11E 
For a distribution from the (a,b,0) class, you are given that and . Find the value of . 
Practice Problem 11F 
You are given that the distribution for the claim count satisfies the following recursive relation: Determine . 
Practice Problem 11G 
Suppose that the random variable is from the (a,b,0) class. You are given that and . Calculate the probability that is at least 3. 
Practice Problem 11H 
For a distribution from the (a,b,0) class, you are given that
Determine . 
Practice Problem 11I 
For a distribution from the (a,b,0) class, you are given that and . Evaluate its mean. 
Practice Problem 11J 
The random variable follows a distribution from the (a,b,0) class. You are given that and . Evaluate . 
Practice Problem 11K 
The random variable follows a distribution from the (a,b,0) class. Suppose that and . Determine . 
Practice Problem 11L 
Given that a discrete distribution is a member of the (a,b,0) class. Which of the following statement(s) are true?
B. ……….. 2 only C. ……….. 3 only D. ……….. 1 and 2 only E. ……….. 1 and 3 only 
Practice Problem 11M 
Given that a discrete distribution is a member of the (a,b,0) class, determine the variance of the distribution if and . 
Practice Problem 11N 
For a distribution in the (a,b,0) class, and . Furthermore, the mean of the distribution is 1. Determine . 
Problem  Answer 

11A 

11B 

11C 

11D 

11E 

11F 

11G 

11H 

11I 

11J 

11K 

11L 

11M 

11N 

Daniel Ma Math
Daniel Ma Mathematics
Actuarial exam
2018 – Dan Ma
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