Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1,000, 5,000, and 10,000, with probabilities 0.84, 0.09, 0.05, and 0.02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge (in dollars)

$560

Explanation:

Calculation for what premium amount should it charge

Using this formula to calculate the premium amount

E(Y)=yxP(y)

Let X variable represent the damage that occured because of accident in the year provided

Based on the information given since the amount deductible is $500 while the expected premium charge is $100 then let defined the premium function as,

For X=0

Hence,

Y=X+$100

For X=1,000, 5,000, and 10,000

Y=X-$500+$100

Y=$400

Let the table below represents probability distribution of y

X= 0, 1,000, 5,000, 10,000

Y= 100 600 4,600 9,600

P(y)=0.84, 0.09, 0.05, 0.02,

(1000-400=600)

(5000-400=4,600)

(10,000-400=9,600)

Now let calculate the PREMIUM AMOUNT to be charge Using this formula

E(Y)=yxP(y)

Let plug in the formula

E(Y)=(100 × 0.84)+( 600 × 0.09) + (4,600 × 0.05) +( 9,600 × 0.02)

E(Y)=84+54+230+192

E(Y)=$560

Therefore the premium amount that it should it charge (in dollars) is $560

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