Posted: March 7th, 2017

You are (hypothetically) an insurer, and you provide medical insurance.

You are (hypothetically) an insurer, and you provide medical insurance. After years of hard work and steady research, you have discovered that the CDF of medical risk of those you insure is always characterized by an exponential distribution. That is, the probability that someone s annual medical expenditures are less than $T is:

Pr(~t < T) = 1 e^( ?T), where ? is that person s risk parameter.
What is the pdf of the risk faced by the person in question?
Would you expect a young person to have a larger ? than an old person?(Hint: the expectation of an exponential random variable is ? 1.)