Re: which one is greater than or equal?
- To: mathgroup at smc.vnet.net
- Subject: [mg41320] Re: [mg41285] which one is greater than or equal?
- From: Bobby Treat <drmajorbob at mailblocks.com>
- Date: Wed, 14 May 2003 08:17:34 -0400 (EDT)
- Sender: owner-wri-mathgroup at wolfram.com
(Step 1) Try some examples and find out.
<< Statistics`DescriptiveStatistics`
a = Table[Random[], {20}];
Sqrt@Mean@a - Mean@Sqrt@a
(Step 2) Look up "convex functions" somewhere, and decide if Sqrt is
convex, concave, or something else.
(Step 3) Look up Jensen's Inequality somewhere.
(Step 4) A simple proof that your function is concave (or convex)
depends on the mean value theorem applied to the derivative. Jensen's
Inequality can be proven by induction.
Bobby
-----Original Message-----
From: Son Bui <shbui at yahoo.com>
To: mathgroup at smc.vnet.net
Subject: [mg41320] [mg41285] which one is greater than or equal?
can any one tell me which one is greater than? Please give your proof.
sqrt((a1+a2+...+an)/n) ? (sqrt(a1)+sqrt(a2)+...+sqrt(an))/n
Bui