Let X denote total medical expenses (in 1000s of dollars) incurred by specific individual throughout a given year. X is approximated by a continuous distribution with the pdf of: f(x)={c(x+4)^(-4), x?0
1. Determine c such that f(x) is the legitimate probability density function. What is the expected total cost of medical expenses per individual? Find E(X).
2. What is the standard deviation of total medical expenses per individual?
3. A person is "flagged" by the insurance company if their expenses are greater than 75% of all other individuals with this policy. What amount of total expenses does an individual need to exceed to be flagged? Find the 75th percentile.
4. For this policy, the insurance company will pay 90% of all medical expenses. If the total cost incurred for an individual in a year is denoted by Y. What is the expectation Y? Meaning, how much should the insurance company expect to pay for a single individual?