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Let X be the damage incurred (in $) in a certain type of accident during a...

Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000 with probabilities .8 .1 .08 and .02 respectively. a particular company offers a $500 deductible policy. if the company wishes its expected profit to be $100 what preminum amount should it charge?
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Answer #1
Concepts and reason

Probability is the state or an extent to which given event is likely to happen. In general, the probability is defined as a number between 0 and 1 where 0 implies the impossibility of an event to occur and 1 implies the certainty of an event to occur.

Fundamentals

The formula used to obtain the premium charge value is,

E(Y)=yxP(y)

Letbe the variable which represents the damage due to certain type of accident in a provided year.

As per provided information, the deductible amount is and the expected premium charge is , then the premium function can be defined as,

ForX = 0 , then

Y = X +100

ForX = 1000, 5000, and 10000 , then

Y = X-500+100

The table represents probability distribution of as,

x y P(y) 0 1000 5000 10000 100 600 4600 9600 0.8 0.1 0.08 0.02

The premium charged is obtained as,

E(Y)= yxP(y) =100x0.8+600x0.1+4600 x 0.08 +9600 x 0.02 = $700

Ans:

The chargeable premium amount is .

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