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The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows. table [ [ Payment (

The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows.
\table[[Payment ($),Probability],[0,0.81],[500,0.08],[1,000,0.04],[3,000,0.03],[5,000,0.02],[8,000,0.01],[10,000,0.01]]
(a) Use the expected collision payment to determine the collision annual insurance premium (in dollars) that would enable the company to break even.
$
(b) The insurance company charges an annual premium of $540 for the collision coverage. What is the expected value of the collision policy (in dollars) for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage.)
$
Why does the policy holder purchase a collision policy with this expected value?
The expected value of the policy is zero indicating on average buying the policy results in a gain for the policy holder.
The expected value of the policy is negative indicating on average buying the policy results in a loss for the policy holder. However, the policy protects the policy holder against a large repair bill in the event of an accident.
The expected value of the policy is positive indicating on average buying the policy results in a gain for the policy holder.
The expected value of the policy is positive indicating on average buying the policy results in a loss for the policy holder. However, the policy protects the policy holder against a large repair bill in the event of an accident.
The expected value of the policy is negative indicating on average buying the pollcy results in a gain for the pollcy holder.
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