1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Unbiased expression?

  1. Jul 26, 2007 #1
    1. The problem statement, all variables and given/known data

    In an example my book says that the expression bellow is unbiased.
    I can't see why this is exactly...

    2. Relevant equations

    [tex]
    \begin{array}{l}
    \hat p = \frac{X}{n} \\\\
    E(\hat p) = E\left( {\frac{X}{n}} \right) = \frac{1}{n} \cdot E(X) = \frac{1}{n} \cdot (n \cdot p) = p \\
    \end{array}
    [/tex]

    3. The attempt at a solution

    Could the reason be that the expression comes down to just p, which is simply a probability and we have no better suggestion than to believe that it "hits the target"? (If that didn't make any sense, just ignore it)
     
  2. jcsd
  3. Jul 26, 2007 #2
    A statistic [itex]\tau(x_1,x_2,...,x_n)[/itex] is said to be unbiased for a parameter [itex]\theta[/itex] if [itex]E[\tau(x_1,x_2,...,x_n)]=\theta[/itex].

    It is just a definition.

    It is important to know that to say that [itex]\hat{p}=\frac{x}{n}[/itex] is unbiased is WRONG. It is unbiased for a particular PARAMETER.

    The expectation of [itex]\hat{p}[/itex] is precisely p. If it so happened that [itex]E[\hat{p}]=p-2[/itex] then [itex]\hat{p}[/itex] would not be an unbiased estimator for p, it would be an unbiased estimator for p-2.
     
    Last edited: Jul 26, 2007
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook




Loading...