Timeline for Expectation of the reciprocal of a standard normal random variable
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Nov 20, 2023 at 13:18 | comment | added | whuber♦ | +1 for the idea, which is excellent and is easily patched up to address the (valid) objections in the comments. For instance, invoke definitions in Lebesgue integration to point out that the expectation is undefined when the positive part of a random variable has a divergent integral. You cannot conclude, however, that $E[1/X]$ is itself infinite! | |
| Nov 20, 2023 at 12:42 | comment | added | Zhanxiong | Note that $1/X$ does not have expectation is very different from $E(1/X) = \infty$. So your conclusion (as well as OP's) is wrong. To see why, the very fist inequality "$E(1/X) > 2P(...)$" is wrong because $X$ is not a non-negative r.v.! | |
| Nov 20, 2023 at 12:01 | comment | added | user225256 | Thank you, @Glen_b, for helping me see through that fog. | |
| Nov 20, 2023 at 11:52 | history | edited | user225256 | CC BY-SA 4.0 |
added 12 characters in body
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| Nov 20, 2023 at 9:40 | comment | added | Glen_b | Seriously, please take another, more careful look at your first line. X cannot be both between 1/4 and a half and between 2 and 4 at the same time. | |
| Nov 20, 2023 at 7:21 | comment | added | user225256 | @kjetilbhalvorsen, I don’t see an error in the first line | |
| Nov 19, 2023 at 23:02 | comment | added | kjetil b halvorsen♦ | You need to review your first line ... | |
| Nov 19, 2023 at 22:59 | history | answered | user225256 | CC BY-SA 4.0 |