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December 25th, 2016, 11:42 AM  #1 
Newbie 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 $\displaystyle p_{\omega>0}=\frac{1p_0}{n}$ 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? 

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