Asymtopic Normality: Let {zi} be a sequence of i.i.d. random variables satisfying the

redwine01

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Hi Guys,

I am having trouble with answering the question in the photo that I have attached. Could you guys help me out? Thanks



Let {zi} be a sequence of i.i.d. random variables satisfying the following:

. . .\(\displaystyle \mathbb{E}(z_i)\, =\, \mu\, \neq\, 0\)

. . .\(\displaystyle var(z_n)\, =\, \sigma^2\)

Let \(\displaystyle \overline{z_n}\) be the sample mean. Show the following:

. . .\(\displaystyle \sqrt{\strut n\,}\, \left(\dfrac{1}{\overline{z_n}}\, -\, \dfrac{1}{\mu}\right)\, \xrightarrow{\,d\,}\, N\, \left(0,\, \dfrac{\sigma^2}{\mu^4}\right)\)
 

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Hi Guys,

I am having trouble with answering the question in the photo that I have attached. Could you guys help me out? Thanks
What are your thoughts?

Please share your work with us ...even if you know it is wrong.

If you are stuck at the beginning tell us and we'll start with the definitions.

You need to read the rules of this forum. Please read the post titled "Read before Posting" at the following URL:

http://www.freemathhelp.com/forum/announcement.php?f=33
 
The problem is I don't have a clue to start with. Where to start with and what to do? if you can show me some direction that would be great
 
The problem is I don't have a clue to start with. Where to start with and what to do? if you can show me some direction that would be great
Have you studied statistics at all? If not, then taking the appropriate sequence of courses would be "where to start". If so, then has your class not yet covered this sort of material? We'll be glad to provide you with lesson links, but we'll need to know how far your class has gotten (and your school's administration may want to know that you're being assigned homework over material that hasn't been taught).

Thank you! ;)
 
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