Let be the damage incurred (in $) in a certain type of accident during a given year. Possible values are , , , and , with probabilities , , , and , respectively. A particular company offers a deductible policy. If the company wishes its expected profit to be , what premium amount should it charge?

Full question attached

Answer and Explanation:

Given probability of damages 0, 1000, 5000, 10000 = 0.8, 0.1, 0.08, 0.02 respectively

Also given that company offers a $500 deductible policy

To find premium amount charged

Equation could be given by

A=X+100 where A is premium charged, X is damage incurred

Substituting 0

A=0+100=100

Substituting 1000

A=1000-500+100=600

Substituting 5000

A=5000-500+100=4600

Substituting 10000

A=10000-500+100=9600

premium amount to be charged

=0.8*100+0.1*600+0.08*4600+0.02*9600 = $700

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