X_n)$?

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Apr 13, 2017 at 12:44	history	edited	CommunityBot		replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
Nov 21, 2012 at 22:43	comment	added	whuber♦		OK, great. Thanks for answering my question about the union bound. (+1)
Nov 21, 2012 at 22:32	comment	added	Dilip Sarwate		@whuber I have incorporated your comments in my revised answer. I wrote out the location-scale transformations because the OP seemed to be not able to recognize that the different means and variances are easily handled, and I agree with your comment on your own answer that the idea applies not just to normal distributions.
Nov 21, 2012 at 22:26	history	edited	Dilip Sarwate	CC BY-SA 3.0	talked about tightness, corrected typo, added definition of $Q(x)$ as pointed out by whuber
Nov 21, 2012 at 22:02	comment	added	whuber♦		(1) How good is the union bound? I would expect it to be poor for $n \ge 3$, because there is so much overlap among the subsets, but I haven't checked. (2) You need to adjust $n$ to $n-1$ in your first integral. (3) I think your notation gets in the way. By writing out the location-scale transformations, you actually make your answer less general than it could be: it is unnecessary to restrict the analysis to such a situation. (4) Presumably, "$Q$" should be the complementary CDF $1-\Phi$ at the end.
Nov 21, 2012 at 21:45	history	answered	Dilip Sarwate	CC BY-SA 3.0