LFD Book Forum Problem 2.14(c)

#1
09-30-2012, 10:50 PM
 mileschen Member Join Date: Sep 2012 Posts: 11
Problem 2.14(c)

For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?
#2
10-01-2012, 04:46 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Problem 2.14(c)

Yes, solving the equation is really hard. It is simpler to show that if takes on the value in the second part of the min, the condition in (b) is satisfied.
Quote:
 Originally Posted by mileschen For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?
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#3
07-14-2014, 05:29 PM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
Re: Problem 2.14(c)

Quote:
 Originally Posted by magdon It is simpler to show that if takes on the value in the second part of the min, the condition in (b) is satisfied.
I have difficulties solving this problem. If I assume that , then the condition in (b) is not satisfied.
(e.g. when , then and ).

I believe the right thing to do would be to assume that because the min bound will still hold and I believe the condition in (b) is then satisfied? But how do I prove that?

I appreciate any help.
#4
07-17-2014, 08:26 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Problem 2.14(c)

There is a typo in the equation, sorry.

The second term in the minimum should be

.

Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if , then the inequality in (b) is satisfied, namely .

Quote:
 Originally Posted by mileschen For Problem 2.14(c), to determine the min value, the way I think would be try to solve the equation in (b) and get L. Maybe L is the second part of the min. However, how to solve the equation is a really hard question. Thus, could anyone tell me how to solve the equation or give me a hint on how to get the right answer?
__________________
Have faith in probability
#5
07-20-2014, 08:48 AM
 BojanVujatovic Member Join Date: Jan 2013 Posts: 13
Re: Problem 2.14(c)

#6
10-01-2015, 07:46 AM
 zhaozb15 Junior Member Join Date: Sep 2015 Posts: 2
Re: Problem 2.14(c)

Quote:
 Originally Posted by magdon There is a typo in the equation, sorry. The second term in the minimum should be . Rather than solve the inequality in (b) to get this bound, you may rather just verify that this is a bound by showing that if , then the inequality in (b) is satisfied, namely .
If , then . Seems not correct
#7
10-06-2015, 09:15 PM
 ilson Member Join Date: Sep 2015 Posts: 10
Re: Problem 2.14(c)

Quote:
 Originally Posted by zhaozb15 If , then . Seems not correct
I came here to say exactly this. Also, if then trivially, so can we assume that ?
#8
10-07-2015, 06:05 AM
 magdon RPI Join Date: Aug 2009 Location: Troy, NY, USA. Posts: 595
Re: Problem 2.14(c)

Quote:
 Originally Posted by ilson I came here to say exactly this. Also, if then trivially, so can we assume that ?
Yes, the problem should state that K>1, otherwise the problem is trivial.
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Have faith in probability
#9
07-12-2017, 10:59 AM
 RicLouRiv Junior Member Join Date: Jun 2017 Posts: 7
Re: Problem 2.14(c)

I'm pretty stuck on this one -- any hints?
#10
05-21-2018, 11:55 AM
 ppaquay Junior Member Join Date: Apr 2018 Location: Liège (Belgium) Posts: 9
Re: Problem 2.14(c)

Hi, I'm also stuck on this one. I don't know if I'm missing an algebraic argument (in verifying that 2^l > 2Kl^d) or if I'm missing something more important. Any hint would be appreciated.

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