Timeline for Expectation for game choosing uniformly number in $[0,1]$ until it decreases
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| Nov 24, 2021 at 4:44 | vote | accept | Shashank Nathani | ||
| Nov 18, 2021 at 0:04 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 17, 2021 at 23:07 | comment | added | Shashank Nathani | @IosifPinelis thanks a lot! This was really helpful. Thank you for your help and patience. | |
| Nov 17, 2021 at 22:44 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 17, 2021 at 22:33 | comment | added | Iosif Pinelis | @ShashankNathani : (i) I did not use conditional expectations anywhere in this answer. (ii) It is not correct to say that I could not use $X_n$ "directly" and therefore had to use $1-X_n$ instead. I just thought that it would be a bit easier to deal with $1-X_n$ first and then with $X_n$, as $1-X_n$ and $X_n$ are very simply related to each other anyway. (iii) However, I have now rewritten the answer without using $1-X_n$. I have also added more details. Are you satisfied now with the answer? | |
| Nov 17, 2021 at 22:21 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 17, 2021 at 15:18 | comment | added | Iosif Pinelis | @ShashankNathani : Do you have any further questions or concerns about this answer? | |
| Nov 16, 2021 at 2:42 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 16, 2021 at 2:40 | comment | added | Iosif Pinelis | @ShashankNathani : The two expressions, $E(1-X_n)\,1(X_1\le\cdots\le X_{n-1}\le X_n)$ and $EX_n\,1(X_1\le\cdots\le X_{n-1}\le X_n)$, are simply related to each other (I have now added a detail on this). However, $E(1-X_n)\,1(X_1\le\cdots\le X_{n-1}\le X_n)$ is more directly expressible in terms of $P(X_1\le\cdots\le X_{n-1}\le X_n\le x)$ than $EX_n\,1(X_1\le\cdots\le X_{n-1}\le X_n)$ is. | |
| Nov 15, 2021 at 20:28 | comment | added | Iosif Pinelis | @DieterKadelka : Thank you for your comment. There indeed was a mistake in my Mathematica programming, which is now fixed, and the results are in agreement. | |
| Nov 15, 2021 at 20:25 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2021 at 20:07 | comment | added | Dieter Kadelka | I think there must be a fault in your program. I just repeated a simulation with numpy (in python) and got $0.35905$. | |
| Nov 15, 2021 at 19:50 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2021 at 19:02 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2021 at 18:53 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2021 at 18:47 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Nov 15, 2021 at 18:41 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |