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 1, with probabilities 0.81, 0.09, 0.08, 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?

$600

Step-by-step explanation:

Let the random variable denote the damage in $ incurred in a certain type of accident during a given year. The probability distribution of is given by

A company offers a $500 deductible policy and it wishes its expected profit to be $100. The premium function is given by

For ,  we have

For ,

For ,

For ,

Therefore, the probability distribution of is given by

To determine the premium amount that the company should charge, we need to calculate the expected value of

Therefore,

which means the $600 is the amount the should be charged.

what is the answer?

what i would say the best answer is a. 40.5