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Question 1 of 10
1. Question
Which type of distribution allows for a heavier tail than the Poisson Process?
Correct
The two-parameter family of negative binomial distributions allows for a heavier tail than the Poisson Process and furthermore it provides a better fit to claim-number data in certain cases as in the example of motor insurance.
Incorrect
The two-parameter family of negative binomial distributions allows for a heavier tail than the Poisson Process and furthermore it provides a better fit to claim-number data in certain cases as in the example of motor insurance.
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Question 2 of 10
2. Question
When is it more appropriate to adopt a binomial distribution for the number of claims?
Correct
When it is appropriate to declare that the number of claims cannot exceed some known number, it can be appropriate to adopt a binomial distribution for the number of claims. This case can arise like when we are dealing with a portfolio consisting of a known number of similar policies on each of which at most a single claim can arise.
Incorrect
When it is appropriate to declare that the number of claims cannot exceed some known number, it can be appropriate to adopt a binomial distribution for the number of claims. This case can arise like when we are dealing with a portfolio consisting of a known number of similar policies on each of which at most a single claim can arise.
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Question 3 of 10
3. Question
The Poisson family of distributions has a single parameter that is denoted by λ (> 0), what does it mean?
Correct
The Poisson family of distributions has a single parameter that is denoted by λ (> 0), which represents the mean of the distribution that means the expected number of claims per unit time in a Poisson process.
Incorrect
The Poisson family of distributions has a single parameter that is denoted by λ (> 0), which represents the mean of the distribution that means the expected number of claims per unit time in a Poisson process.
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Question 4 of 10
4. Question
What is the sum of independent Poisson random variables?
Correct
The sum of independent Poisson random variables is a Poisson random variable with a mean equal to the sum of the component means.
Incorrect
The sum of independent Poisson random variables is a Poisson random variable with a mean equal to the sum of the component means.
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Question 5 of 10
5. Question
What are the three properties included in a Poisson process?
Correct
A process that satisfies the three properties is called a Poisson process with rate. The first one is independent increments, the second one being the stationary increments and the Poisson distribution.
Incorrect
A process that satisfies the three properties is called a Poisson process with rate. The first one is independent increments, the second one being the stationary increments and the Poisson distribution.
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Question 6 of 10
6. Question
The third central moment is given by [kq(2 − p)]/p3, For fixed p, what happens when the coefficient of skewness decreases?
Correct
The third central moment is given by [kq(2 − p)]/p3. It follows that the coefficient of skewness, as the distribution is always positive. For fixed p, the coefficient of skewness decreases as k increases, and the distribution becomes more symmetrical.
Incorrect
The third central moment is given by [kq(2 − p)]/p3. It follows that the coefficient of skewness, as the distribution is always positive. For fixed p, the coefficient of skewness decreases as k increases, and the distribution becomes more symmetrical.
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Question 7 of 10
7. Question
The third central moment is given by [kq(2 − p)]/p3. For fixed k, what happens if the p increases?
Correct
The third central moment is given by [kq(2 − p)]/p3. It follows that the coefficient of skewness for the distribution is always positive. For fixed k, the coefficient of skewness increases as p increases.
Incorrect
The third central moment is given by [kq(2 − p)]/p3. It follows that the coefficient of skewness for the distribution is always positive. For fixed k, the coefficient of skewness increases as p increases.
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Question 8 of 10
8. Question
How does the model of the geometric family work?
Correct
The distribution models the number of failures that occur before the first success in a series of independent Bernoulli trials, each with success probability p.
Incorrect
The distribution models the number of failures that occur before the first success in a series of independent Bernoulli trials, each with success probability p.
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Question 9 of 10
9. Question
The geometric family is a sub-family of which family in the distribution of claims?
Correct
The geometric family is a sub-family of the negative binomial family, namely the special case. The distribution models the number of failures that occur before the first success in a series of independent Bernoulli trials, each with success probability p.
Incorrect
The geometric family is a sub-family of the negative binomial family, namely the special case. The distribution models the number of failures that occur before the first success in a series of independent Bernoulli trials, each with success probability p.
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Question 10 of 10
10. Question
How many parameters does the geometric family have, when used in claim-distribution?
Correct
The geometric family is a sub-family of the negative binomial family and the geometric family has a single parameter that is denoted p when 0 < p < 1.
Incorrect
The geometric family is a sub-family of the negative binomial family and the geometric family has a single parameter that is denoted p when 0 < p < 1.