Results 1 to 2 of 2

Math Help - Biased/Unbiased help

  1. #1
    Super Member craig's Avatar
    Joined
    Apr 2008
    Posts
    748
    Thanks
    1
    Awards
    1

    Biased/Unbiased help

    Hi, if someone could take a look through and help me on this problem it would me much appreciated.

    Note all the following distributions have sample size 9.

    Let X - N(\mu, 0.3^2) and Y - N(\mu, 0.6^2).

    We then form the following distributions:

    U = \frac{1}{2}X + \frac{1}{2}Y

    V = \frac{2}{3}X + \frac{1}{3}Y

    W = \frac{4}{5}X + \frac{1}{5}Y

    In each of the above cases work out the sampling distribution of the estimator, explain whether it's unbiased and give the standard error.

    Here's what I've managed to do so far:

    U - N(\mu, 0.45^2)

    V - N(\mu, 0.4^2)

    W - N(\mu, 0.36^2)

    Using the fact that \bar{X} - N(\mu, \frac{\sigma^2}{n}), and with a sample size of 9, we can then get the sampling distributions of the 3 estimators:

    \bar{U} - N(\mu, \frac{9}{400})

    \bar{V} - N(\mu, \frac{4}{225})

    \bar{W} - N(\mu, \frac{9}{625})

    I think these are right, please correct me if I've made a mistake somewhere.

    Now the standard error of the estimator is \frac{\sigma}{\sqrt{n}}, giving us

    SE \bar{U} = \frac{3}{20}

    SE \bar{V} = \frac{2}{15}

    SE \bar{W} = \frac{3}{25}

    I think this is correct up to here. The only thing I'm really stuck on is how to find whether they are biased or unbiased?

    Thanks in advance

    Craig
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Member
    Joined
    Oct 2009
    Posts
    218
    Let's say we want to know if a statistic Y is a biased/unbiased estimator for \theta.

    If E(Y_1)=\theta then Y is an unbiased estimator of \theta

    Now if E(Y_2) = n \theta then Y is a biased estimator of \theta.

    E(\frac{Y_2}{n}) = \theta then Y2 is an unbiased estimator of \theta

    I'm assuming you need to determine if a statistic is an unbiased estimator of \mu since it's the only unknown variable you have.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] maximum likelihood estimator biased not unbiased
    Posted in the Calculus Forum
    Replies: 1
    Last Post: August 16th 2010, 03:33 AM
  2. biased?
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: March 9th 2010, 10:09 PM
  3. biased and unbiased
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: December 20th 2009, 07:57 AM
  4. determing unbiased or biased estimator
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: June 5th 2009, 01:58 PM
  5. how do u show this MLE is biased
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: February 4th 2009, 05:07 PM

Search Tags


/mathhelpforum @mathhelpforum