(adsbygoogle = window.adsbygoogle || []).push({}); 1. Essentially what I'm trying to do is find the asymptotic distributions for

a)

Y^{2}

b) 1/Y and

c) e^{Y}where

Y = sample mean of a random iid sample of size n.

E(X) = u; V(X) = σ_{2}

2. Relevant equations

a) [tex]Y^2=Y*Y[/tex] which converges in probability to [tex]u^2[/tex],

[tex]V(Y*Y)=\sigma^4 + 2\sigma^2u^2[/tex]

So, [tex]\sqrt{n}*(Y^2 - u^2)[/tex] converges in probability to [tex]N(0,\sigma^4 + 2\sigma^2u^2) [/tex]

So, [tex]Y^2\sim N(u^2,\frac{\sigma^4 + 2\sigma^2u^2}{n})[/tex]

Is that right?

b) [tex]\frac{1}{Y}[/tex] converges in probability to [tex]\frac{1}{E(X)} = \frac{1}{u}[/tex]

[tex]V(\frac{1}{x}) = \frac{1}{σ^2}[/tex] ??

Thus,

[tex]\sqrt{n}(\frac{1}{Y} - \frac{1}{u})[/tex] converges in distribution to [tex]N(0,V(\frac{1}{x})*\frac{1}{n})[/tex]

What is V(1/X) ?

Am I on the right track?

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# Homework Help: Calculating Variances of Functions of Sample Mean

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