Thread: Strong Law of Large Numbers

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

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.

Originally Posted by matheagle

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.

with the function provided, how do I compute the expected MPG? Can you provide an example?

$\displaystyle f(z)=.1$ on $\displaystyle 5\le z <8$

and

$\displaystyle f(z)= {1\over 8}e^{-z/8}$ on $\displaystyle z \ge 8$

SO $\displaystyle E(Z)=.1\int_5^8 zdz + {1\over 8}\int_8^{\infty} ze^{-z/8}dz$

HOWEVER I don't think this is a valid distribution function.
There are jumps and it seems to be a continuous setting.
So something is off.