Timeline for Conditional Expectation of Order Statistic [duplicate]
Current License: CC BY-SA 3.0
5 events
| when toggle format | what | by | license | comment | |
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| Dec 14, 2017 at 0:20 | comment | added | Mitch Baker | Thanks! I suspected as much. The two remaining variates are uniformly distributed on the interval staked out by the minimum and maximum. Then all that is necessary is to look at the density of minimal order statistic, say $V$, on said interval and compute $\mathbb{E}(V)$. Thanks again! | |
| Dec 13, 2017 at 23:43 | history | closed | whuber♦ | Duplicate of Estimator by Rao Blackwellization (check logic and solution) | |
| Dec 13, 2017 at 23:00 | comment | added | jbowman | I am assuming this is homework or self-study, so will give a hint: given $X_{(1)}$ and $X_{(4)}$, what distribution do each of the remaining two variates have, unconditional upon order? Given that, the next step is to work out the distribution of the smaller of the two variates, and from that get to the expected value. | |
| Dec 13, 2017 at 22:51 | history | edited | Taylor | CC BY-SA 3.0 |
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| Dec 13, 2017 at 22:17 | history | asked | Mitch Baker | CC BY-SA 3.0 |