**Determining Insurance Premiums: A Break-Even Analysis****Scenario:**A customer holds a home insurance policy for a property valued at $200,000. The likelihood of the property being completely destroyed by fire is 0.1%, while there is a 0.5% chance that the property will incur a 50% loss due to fire. In this analysis, other partial losses are not considered. The insurance company's objective is to determine the premium needed for the policy to break even.**Objective:**Calculate the insurance premium required for the policy to break even.**Variable Definition:**$ X $ = the amount of compensation paid to the customer.**Approach:**Leverage the probability distribution table to ascertain the sample space for the random variable $ X $.**Hint:**Use the probability distribution table that has been created to find the outcomes and probabilities associated with $ X $. This helps in calculating the expected compensation, allowing the determination of the break-even premium.

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Calculate the premium that the insurance company should charge for a policy to break even.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.

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Question

**Determining Insurance Premiums: A Break-Even Analysis**

**Scenario:**

A customer holds a home insurance policy for a property valued at $200,000. The likelihood of the property being completely destroyed by fire is 0.1%, while there is a 0.5% chance that the property will incur a 50% loss due to fire. In this analysis, other partial losses are not considered. The insurance company's objective is to determine the premium needed for the policy to break even.

**Objective:**

Calculate the insurance premium required for the policy to break even.

**Variable Definition:**

$ X $ = the amount of compensation paid to the customer.

**Approach:**

Leverage the probability distribution table to ascertain the sample space for the random variable $ X $.

**Hint:**

Use the probability distribution table that has been created to find the outcomes and probabilities associated with $ X $. This helps in calculating the expected compensation, allowing the determination of the break-even premium.

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