Timeline for Mean and variance of the reciprocal of a random variable
Current License: CC BY-SA 4.0
13 events
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| Dec 28, 2023 at 17:14 | comment | added | kjetil b halvorsen♦ | @linguisticturn:n What is the practical value of existence in principal value sense? | |
| Jul 28, 2021 at 16:15 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 27, 2021 at 18:43 | comment | added | whuber♦ | Those are good questions. One can answer them by studying the Normal distribution, using calculations similar to the one I used in my first comment. | |
| Jul 27, 2021 at 18:40 | comment | added | linguisticturn | @whuber Yes, but that raises the following question: what, precisely, is the correct probability-theory interpretation of the 'analytic formula for' E(Y^2)? Equivalently, what is the probability-theory interpretation of the 'counterterm'? And also it raises this practical question: suppose we will be taking samples of size N. Suppose the sigma (the standard deviation) of the normal distribution is given. How small can the mu (the mean) of the normal distribution get before we have to start to worry that E(Y^2) will start to become unpredictable? (Or, for a given mu, how large an N?) | |
| Jul 26, 2021 at 17:51 | comment | added | whuber♦ | This looks interesting, thank you. However, I stopped reading closely about a quarter of the way in after noting that even a huge Monte-Carlo sample from $N(0.9, 0.1)$ will almost never sample even a single negative value. (You would need to draw around $10^{19}$ values before seeing a negative number.) Thus, you are effectively truncating these distributions and there consequently is no mystery why any of the expectations will exist and be finite. I think this might have useful applications, but that possibility seems buried under what ultimately looks like superfluous mathematics. | |
| Jul 26, 2021 at 13:25 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 26, 2021 at 5:26 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 26, 2021 at 5:18 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 26, 2021 at 4:57 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 26, 2021 at 4:18 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 25, 2021 at 21:50 | history | edited | linguisticturn | CC BY-SA 4.0 |
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| Jul 25, 2021 at 21:47 | review | First posts | |||
| Jul 26, 2021 at 3:14 | |||||
| Jul 25, 2021 at 21:41 | history | answered | linguisticturn | CC BY-SA 4.0 |