"Let Xsub1, Xsub2,.....Xsubn be a random sample from a Uniform distribution U(Theta, Theta+1)

It is known that, E(Xsub1)=Theta+1/2, V(Xsub1)=1/12"

(a)"Show that Xbar is NOT unbiased for theta. what is its bias?"

(b) "Based on (a), construct an unbiased estimator for Theta using Xbar

(c) "Compute V(Xbar), V(Xsub1-1/2), and the variance of the estimator you constructed in (b).

im stuck, i know that for all dis. E(Xbar)= mu

but how does that pertain to E(Xsub1)=Theta+1/2?

if someone could point me in the right direction, im sure i can figure out b and c

im just completely stuck right now

5/4/2006 9:46:27 PM

Reading that just broke my head even more.

5/4/2006 9:46:59 PM

The bias is that the mean is .5 more than theta?

If that's not it, I don't have a clue.

5/4/2006 9:57:24 PM

5/4/2006 9:58:41 PM

thats what i was thinking

but im just a dumb gimp

5/4/2006 9:58:59 PM

Gimptastic

5/4/2006 10:01:04 PM

never mind

[Edited on May 4, 2006 at 11:20 PM. Reason : adsdfda]

5/4/2006 11:15:15 PM

gimp_{You're premie. Use the sub tags.}

5/4/2006 11:18:17 PM

yea

i was lazy

5/4/2006 11:19:10 PM

a) E(Xi) = E(X-bar) = theta + .5 so Bias = E(X-bar) - theta = 1/2

b) An unbiased estimator for theta using x bar is then x-bar - 1/2 since E(x-bar - 1/2) = theta

c) V(Xbar) = V(Xi) / n = 1/12n

The next part I'm a little fuzzy on.
The X's are from a random sample so they are indepedent.
V(Xbar - 1/2) = V(Xbar) - 1/2 = 1/12n - 1/2

I remember doing this problem earlier this year. Are you in 422 with Gerig.

5/4/2006 11:20:08 PM

yea thats what i figured out too, ty for the help, i had nothing to check it with

na im in 372

5/4/2006 11:22:24 PM