# Getting a new distribution for X(bar)

• Apr 6th 2010, 03:24 PM
xoyankeegirlx3
Getting a new distribution for X(bar)
Let X(bar) be the mean of a random sample of size 12 from the uniform distribution on the interval (0,1).
Approximate P(1/2 < X(bar) < 2/3).

No idea how to do this whatsoever.
I know you can use the moment generating function but I can't simplify it to make it work.
And sorry I can't overscore? on here, so X(bar) is sample mean.

Also, a general idea of how to approach these problems would be helpful too, I have other similar practice problems.

Any help would be greatly appreciated.
• Apr 6th 2010, 04:30 PM
matheagle
The sum of uniforms is not a uniform so I had expected a central limit problem here.
But with n=12 that's not really appropriate.
you can multiply by 12 and then figure out

$P\left(6<\sum_{i=1}^{12} X_i<8\right)$

which is a 12 fold integral with density 1.
• Apr 7th 2010, 06:42 PM
xoyankeegirlx3
Quote:

Originally Posted by matheagle
The sum of uniforms is not a uniform so I had expected a central limit problem here.
But with n=12 that's not really appropriate.
you can multiply by 12 and then figure out

$P\left(6<\sum_{i=1}^{12} X_i<8\right)$

which is a 12 fold integral with density 1.

That makes sense, thanks for the help!
• Apr 7th 2010, 08:28 PM
matheagle
BUt it still is a pain in the..........