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Apr 10 at 17:47 history edited knrumsey CC BY-SA 4.0
An edit to expand upon the OPs empirical observations.
Nov 21, 2019 at 16:22 review Suggested edits
Nov 21, 2019 at 16:28
Nov 21, 2019 at 13:37 vote accept KaPy3141
Nov 20, 2019 at 21:29 history edited knrumsey CC BY-SA 4.0
added 3 characters in body
Nov 20, 2019 at 21:00 history edited knrumsey CC BY-SA 4.0
added an assumption and fixed direction of inequality.
Nov 20, 2019 at 20:42 comment added Sextus Empiricus So, this method requires m>n.
Nov 20, 2019 at 20:32 comment added COOLSerdash @SextusEmpiricus Thanks! With your hint about the triangle, I was able to work out the other way just now. Many thanks.
Nov 20, 2019 at 20:30 comment added Sextus Empiricus This is another way $$ P(Y \geq cX) = \int_0^{1} \left( \int_{0}^{y/c} nmx^{n-1}y^{m-1}dx \right) dy $$
Nov 20, 2019 at 20:27 comment added Sextus Empiricus This is actually the integral for $P(y > cx)$
Nov 20, 2019 at 20:20 comment added Sextus Empiricus @COOLSerdash it is scanning the triangle where y < cx. You can do this in two directions. This one scans the lines cx < y < 1. And x goes from 0 to 1/c.
Nov 20, 2019 at 20:09 comment added COOLSerdash (+1) Great! May I ask how you found the limits of integration for the joint density?
Nov 20, 2019 at 19:49 history edited knrumsey CC BY-SA 4.0
added link to order statistic result
Nov 20, 2019 at 19:43 history undeleted knrumsey
Nov 20, 2019 at 19:43 history edited knrumsey CC BY-SA 4.0
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Nov 20, 2019 at 18:53 history deleted knrumsey via Vote
Nov 20, 2019 at 18:51 history edited knrumsey CC BY-SA 4.0
added 366 characters in body
Nov 20, 2019 at 18:43 history answered knrumsey CC BY-SA 4.0