Timeline for What is the meaning of big-O of a random variable?
Current License: CC BY-SA 4.0
9 events
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| Dec 22, 2022 at 5:19 | comment | added | zzzhhh | @Carlo Beenakker: Thank you. As you commented, I think $O(\xi^3)$ here has nothing to do with regular big-O notation. It is only "a sloppy notation" meaning that it is a small number (a third or second moment of $\xi$ multiplied by a finite integral which is still small by assumption), so it can be discarded safely. | |
| Dec 21, 2022 at 15:03 | comment | added | Carlo Beenakker | the point I want to make is that it makes no sense to write $\mathbb E[\xi^2]=O(\xi^2)$ ; it should be $\mathbb E[\xi^2]=O(\sigma^2)$, I presume this is just a sloppy notation of the author. | |
| Dec 21, 2022 at 10:38 | comment | added | zzzhhh | @Carlo Beenakker: Since the distribution of $\xi$ has a zero mean and small variance, $\xi$ is also small most of the time, hence $\xi^3$, $O(\xi^3)$ and the integral of $(1)$. I just cannot formulate this idea rigorously in math. | |
| Dec 21, 2022 at 9:01 | comment | added | Carlo Beenakker | I presume that the author means ${\cal O}(\sigma^3)$ rather than ${\cal O}(\xi^3)$, where $\sigma^2$ is the variance of $\xi$ (assumed to be small) | |
| Dec 21, 2022 at 8:19 | review | Close votes | |||
| Jan 5, 2023 at 3:06 | |||||
| Dec 21, 2022 at 7:46 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Math Jaxing (formula hyperlinking)
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| Dec 21, 2022 at 7:40 | history | edited | zzzhhh | CC BY-SA 4.0 |
deleted 2 characters in body
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| S Dec 21, 2022 at 7:31 | review | First questions | |||
| Dec 21, 2022 at 15:16 | |||||
| S Dec 21, 2022 at 7:31 | history | asked | zzzhhh | CC BY-SA 4.0 |