Timeline for Finding the distribution of $2\theta X_i^2$
Current License: CC BY-SA 4.0
15 events
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| S Jun 15, 2023 at 16:14 | history | suggested | Starship | CC BY-SA 4.0 |
removed "Thanks in Adavanced"
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| Jun 15, 2023 at 12:32 | review | Suggested edits | |||
| S Jun 15, 2023 at 16:14 | |||||
| Dec 14, 2017 at 23:04 | comment | added | Gordon Smyth | One last hint. $\sum 2\theta X^2_i$ follows a chi-square distribution, but not on $n$ df. You figure out the df. | |
| Dec 14, 2017 at 18:58 | comment | added | Gordon Smyth | $2\theta X^2_i$ is obviously a strictly positive quantity. I wonder how you expected to show that a strictly positive random variable follows a $N(0,1)$ distribution? That should have been ringing alarm bells for you. | |
| Dec 14, 2017 at 18:28 | comment | added | Gordon Smyth | Pivoting and normality have nothing at all to do with one another. A pivot is just a random variable whose distribution doesn't depend on $\theta$. There is no requirement for it to follow a normal, or any other, distribution. (Surely you could have found out for yourself, either from the course notes or from google en.wikipedia.org/wiki/Pivotal_quantity .) | |
| Dec 14, 2017 at 1:24 | vote | accept | Silvia Rossi | ||
| Dec 14, 2017 at 0:48 | answer | added | Deep North | timeline score: 1 | |
| Dec 14, 2017 at 0:40 | comment | added | Silvia Rossi | Thank you very much, I will do that. But how would I show that $\sum 2 \theta X_i^2$ is a pivot if it does not have $N(0,1)$ distribution? @GordonSmyth | |
| Dec 13, 2017 at 23:55 | comment | added | Gordon Smyth | Just apply the transformation $y=x^2$. You will find that $y$ has a very simple well-known distribution. You will not however be able to show that $\sum 2\theta X_i^2\sim N(0,1)$ because it is simply not true. | |
| Dec 13, 2017 at 23:16 | history | edited | Silvia Rossi | CC BY-SA 3.0 |
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| Dec 13, 2017 at 22:50 | history | edited | Silvia Rossi | CC BY-SA 3.0 |
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| Dec 13, 2017 at 22:49 | history | edited | Taylor | CC BY-SA 3.0 |
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| Dec 13, 2017 at 22:37 | history | edited | Silvia Rossi |
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| Dec 13, 2017 at 22:35 | comment | added | Michael R. Chernick | Add the self study tag. | |
| Dec 13, 2017 at 22:29 | history | asked | Silvia Rossi | CC BY-SA 3.0 |