Timeline for Sample Mean expressed using Standard Normal Distribution
Current License: CC BY-SA 4.0
5 events
| when toggle format | what | by | license | comment | |
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| Feb 24, 2019 at 11:16 | comment | added | gunes | Yes, and it also applies the fact that normal RVs are still normal under linear transformation. Other RVs may not satisfy this property. For example, if $X$ is Bernoulli, $2X$ is not Bernoulli. | |
| Feb 24, 2019 at 11:13 | comment | added | user11128 | Basically just applying Var(cX) = c^2 Var(X)? | |
| Feb 24, 2019 at 11:10 | comment | added | gunes | This doesn't show $\bar{X_n}=\frac{1}{\sqrt{n}}Z$, but I tried to answer your title question. For this one, in the notes, $\bar{X_n}$ is defined that way via $\overset{d}=$ operator. So, it's basically saying that if $\bar{X_n}$ is Normal with $(0,1/n)$, then a standard normal RV can be defined such that $\bar{X_n}=\frac{1}{\sqrt{n}}Z$. | |
| Feb 24, 2019 at 10:53 | comment | added | user11128 | Thanks. I follow your result that the x pdf can be written in terms of $\phi(x)^n$ but how does this show $\bqr{X}_n = n^{-1/2} Z$? See second to last line of page 1 in these notes for the claim: www.stat.cmu.edu/~larry/=stat705/Lecture2.pdf | |
| Feb 24, 2019 at 9:48 | history | answered | gunes | CC BY-SA 4.0 |