Strong Law of Large Numbers

**noles2188** · Nov 10th 2009, 10:01 AM

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

**matheagle** · Nov 10th 2009, 10:42 PM

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.

**noles2188** · Nov 10th 2009, 10:56 PM

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?

**matheagle** · Nov 10th 2009, 11:04 PM

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

and

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

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

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.

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