An insurance company uses a random variable X to describe th

An insurance company uses a random variable X to describe the actual cost of an accident incurred by a female driver who is 20 to 30 years old. A second random variable Y models the actual cost of an accident by a male driver in the same range of ages. Both random variables are measured in dollars. Mark the statement true or false. If you believe that the statement is false, briefly say why you think it is false.

If costs associated with accidents rise next year by 5%, then the mean of the random variable X should also increase by 5%.

Choose the correct answer below.

A.

False. The 5% increase in the costs associated with accidents more likely applies to variable Y than to variable X.

B.

True

C.

False. The distribution may be skewed and the expected value may rise by more or less than the 5% increase.

D.

False. The mean of the random variable X should increase by 2.5%.

Solution

Option (C) is correct, we cannot say anything without knowing the distribution of accidents between the two genders.