Thread: A random sample X

1. A random sample X

Question : A random sample $X_1,X_2,X_3 ..... X_n$ is taken. Show that the sample mean $\bar X$ is an unbiased estimate of the population mean $\mu$

2. Originally Posted by zorro
Question : A random sample $X_1,X_2,X_3 ..... X_n$ is taken. Show that the sample mean $\bar X$ is an unbiased estimate of the population mean $\mu$
You will find the proof in almost any Stats textbook and undoubtedly Google will turn up proofs in abundance. Also, see here:http://www.mathhelpforum.com/math-he...stimators.html (and no doubt using the Search tool will turn up more threads).

3. I was able to find one but dont know if its correct or no

Originally Posted by mr fantastic
You will find the proof in almost any Stats textbook and undoubtedly Google will turn up proofs in abundance. Also, see here:http://www.mathhelpforum.com/math-he...stimators.html (and no doubt using the Search tool will turn up more threads).

Since $f(x) = \frac{1}{ \sigma \sqrt{2 \pi}} . e^{- \frac{(x- \mu)^2}{2 \sigma}}$

it follows that

$ln f(x) = - ln \ \sigma \sqrt{2 \pi} - \frac{1}{2} \left( \frac{x- \mu}{\sigma} \right)^2
$

so that

..
..
....
$= \frac{\sigma^2}{n}$..............Is the theorem u were talking about???

4. Originally Posted by zorro
Since $f(x) = \frac{1}{ \sigma \sqrt{2 \pi}} . e^{- \frac{(x- \mu)^2}{2 \sigma}}$

it follows that

$ln f(x) = - ln \ \sigma \sqrt{2 \pi} - \frac{1}{2} \left( \frac{x- \mu}{\sigma} \right)^2
$

so that

..
..
....
$= \frac{\sigma^2}{n}$..............Is the theorem u were talking about???
I have no idea how you would think I was talking about anything like that. Did you click on the link in my first post? Have you done a Google search? Key words: mean unbiased estimator

5. thanks Mr fantastic ......
i have got it now .......Thank u