Answer:
Replacing the values that we have:
And solving for a we got:
So then the premium value for the insurance on this case should be 1840 dollars.
Explanation:
For this case we can define the random variable X as the gain ( in thousand of dollars) of insurance company
We assume that the premium clase charge and amount of a to the company and we know from the info given that:
represent the expected gain in thousand of dollars
The expected value of a random variable X is the n-th moment about zero of a probability density function f(x) if X is continuous, or the weighted average for a discrete probability distribution, if X is discrete.
And using the definition for a discrete random variable we know that :
Replacing the values that we have:
And solving for a we got:
So then the premium value for the insurance on this case should be 1840 dollars.