An insurance company will sell a fire insurance policy for a house similar to mine for $1000 (for one year of protection). if there is not a fire at my house this year, the insurance company has made a $1000 profit. their experience indicates that there is a .001 probability that I will have a "total"" loss fire costing them $301,000 (meaning that they collected $1000 from me at the beginning of the year, and paid $301,000 to rebuild my home and replace loss contents during th year - a huge loss for them). there is a 1% chance that I'll have a "small" fire which will casuse $41,000 in damages. Suppose that these are the only possible outcomes in this simplified example.Fill in this table to help you answer the questions below.                          d) the mean shows that writing many fire insurance policies like this is good business for the insurance company, explain why. e) the standard deviation provides some indication as to why it would be a bad idea for me to insure someone's home myself in the same manner that the insurance company provides protection against financial loss from a fire. Explain why.

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Asked Sep 12, 2019
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An insurance company will sell a fire insurance policy for a house similar to mine for $1000 (for one year of protection). if there is not a fire at my house this year, the insurance company has made a $1000 profit. their experience indicates that there is a .001 probability that I will have a "total"" loss fire costing them $301,000 (meaning that they collected $1000 from me at the beginning of the year, and paid $301,000 to rebuild my home and replace loss contents during th year - a huge loss for them). there is a 1% chance that I'll have a "small" fire which will casuse $41,000 in damages. Suppose that these are the only possible outcomes in this simplified example.

Fill in this table to help you answer the questions below.


         
         
         
         
         

 

d) the mean shows that writing many fire insurance policies like this is good business for the insurance company, explain why.

 

e) the standard deviation provides some indication as to why it would be a bad idea for me to insure someone's home myself in the same manner that the insurance company provides protection against financial loss from a fire. Explain why. 

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Expert Answer

Step 1

The table is shown below

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P(X) х Fire 0.001 1000-301000= - 300000 Small 0.01 1000-41000= -40000 fire No fire 0.989 1000

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Step 2

Required probability that insurance company will be in profit i.e there will be no fire = 1-0.01-0.001= 0.989

a) Expected value for f...

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-40000) 0.001 x (-300000) 289 Еxpected valuе 0.989 х 1000 + 0.01 х

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