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:
. . .\(\displaystyle \sqrt{\strut n\,}\, \left(\dfrac{1}{\overline{z_n}}\, -\, \dfrac{1}{\mu}\right)\, \xrightarrow{\,d\,}\, N\, \left(0,\, \dfrac{\sigma^2}{\mu^4}\right)\)
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:
. . .\(\displaystyle \sqrt{\strut n\,}\, \left(\dfrac{1}{\overline{z_n}}\, -\, \dfrac{1}{\mu}\right)\, \xrightarrow{\,d\,}\, N\, \left(0,\, \dfrac{\sigma^2}{\mu^4}\right)\)
Attachments
Last edited by a moderator: