An insurance company found that 2.5% of male drivers between the ages of 18 to 25 are involved in serious accidents annually. To simplify the analysis, assume (artificially) the following: 1) every such accident costs the insurance company \$50,000; 2) a driver can only have one of these accidents in a year; 3) the insurer charges $2,000 for a policy; 4) the accidents occur independently of each other.
Suppose that the company writes 1,000 such policies to a collection of drivers as described above. Describe the total payments from these policies by the random variable Y. What are the expected value and SD of Y?
So far I have that E(Y) = (25)(-50,000) + (975)(2000) = 700,000. Is this right, and how do I find the SD? Also, from the insurer's point of view, is the expected value of an individual policy = (2000) - (50,000 x .025) = 750?