I'm not sure what beta is here.
BUT all I think they want you to do is compute the expected MPG.
The sample mean converges to this population mean is the point.
The distribution function F(z) =
{0 if z< 5
{z/10 if 5 <= z < 8
{1-e^(-z/8) if 8 <= z
is associated with the MPG of a car. Using the Strong Law of Large Numbers, what may be the MPG?
Where should I start this problem and how would I go about using the Strong Law of Large Numbers? Would the expected cost be E(|z-beta|)? Any help would be appreciated