Hint$($s$)$

Check My Work

The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance follows.

$\backslash$table$[[$Payment $($$$),$Probability$],[0,0\mathrm{.}85],[500,0\mathrm{.}04],[1,000,0\mathrm{.}04],[3,000,0\mathrm{.}03],[5,000,0\mathrm{.}02],[8,000,0\mathrm{.}01],[10,000,0\mathrm{.}01]]$

$($a$)$ Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. If required, round your answers to two decimal places. If your answer is zero, enter $"0".$

$($b$)$ The insurance company charges an annual rate of $$520$ for the collision coverage. What is the expected value of the collision policy for a policyholder? $($Hint: It is the expected payments from the company minus the cost of coverage.$)$ If required, enter negative value as negative number.