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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


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