My Math Forum  

Go Back   My Math Forum > College Math Forum > Advanced Statistics

Advanced Statistics Advanced Probability and Statistics Math Forum

LinkBack Thread Tools Display Modes
December 25th, 2016, 10:42 AM   #1
Joined: Dec 2016
From: US

Posts: 6
Thanks: 0

Information Theory exercise

Anyone could please tell me how to solve this exercise?

Let there be $\displaystyle n+1$ boxes labeled $\displaystyle \omega=1,2,...,n$. One of the boxes contains a
prize, the others are empty. The probability $\displaystyle p_0$ that the prize is in $\displaystyle \omega=0$ is much
larger than the probability that it is in any other box: $\displaystyle p_0>>p_{\omega>0}$ and we take
$\displaystyle p_{\omega>0}=\frac{1-p_0}{n}$ for simplicity. Note that, if $\displaystyle n$ is large, $\displaystyle p_0$ can nonetheless be also small.
There are two possible options:

1) open the box $\displaystyle \omega=0$;
2) open simultaneously all boxes $\displaystyle \omega>\frac{n}{2}$ (imagine $\displaystyle n$ is even).
Which one is the most convenient? Which one conveys most information on where the prize actually is?
mike22 is offline  

  My Math Forum > College Math Forum > Advanced Statistics

exercise, information, theory

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Information Theory exercise mike22 Probability and Statistics 1 December 25th, 2016 07:59 PM
Evil integral in theory of information formula binek Calculus 0 October 15th, 2011 05:38 AM
Model theory exercise oigroig Applied Math 0 May 7th, 2011 10:15 AM
the exercise presents numerical information ? kiwimath Algebra 1 July 17th, 2009 09:40 AM
Entropy (information theory) trid2 Advanced Statistics 1 March 1st, 2009 06:24 PM

Copyright © 2018 My Math Forum. All rights reserved.