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#11
01-20-2013, 03:58 AM
 alinsoar Member Join Date: Jan 2013 Posts: 17
Re: Q1 and Q2

I will re-phrase the problem 2 with my own words :

We have 1000 bins, and we make 100K experiments of extraction of samples of 10 elements each (with replacement). Each bin has inside it 2 symbols: 'head and 'tail.

Are we allowed to apply the Hoeffding inequality in the following situations:

1. all samples are extracted from the same bin

2. each sample is extracted from a randomly bin

3. each sample is extracted from the bin that provided at the Kth experiment the minimal freq. of heads.

Am I right to think the problem so or am I wrong ?

In my case, which is the hypothesis set ?
#12
01-20-2013, 06:04 AM
 palmipede Member Join Date: Jan 2013 Posts: 13
Re: Q1 and Q2

For Q1, the exact distribution of n_min can be computed and the analytical answer matches my empirical answer but none of the listed answers exactly.
#13
01-20-2013, 07:09 AM
 alinsoar Member Join Date: Jan 2013 Posts: 17
Re: Q1 and Q2

Quote:
 Originally Posted by palmipede For Q1, the exact distribution of n_min can be computed and the analytical answer matches my empirical answer but none of the listed answers exactly.

For me it does , read closely : νmin is closest to:
#14
04-12-2013, 10:57 AM
 jlaurentum Member Join Date: Apr 2013 Location: Venezuela Posts: 41
Re: Q1 and Q2

Hello:

I understand that the mu's are the expected values the relative frequency of heads in N=10 flips. Clearly, mu_1=mu_crand=0.5. Mu_min is different from this value, but it can be calculated analytically. I found that all three sample frequencies (nu's) converge to their respective mu values for all three coins, regardless of whether one coin is fixed and the other 2 sample frequencies are obtained by looking at the 1000*10 flips. This is to be expected, as the law of large numbers states that all sample frequencies converge to the true population frequencies. However, there is no option in question 2 for "all three coins satisfy hoeffding's inequality". Where is my error?
#15
04-12-2013, 11:52 AM
 yaser Caltech Join Date: Aug 2009 Location: Pasadena, California, USA Posts: 1,477
Re: Q1 and Q2

Quote:
 Originally Posted by jlaurentum Hello: I understand that the mu's are the expected values the relative frequency of heads in N=10 flips. Clearly, mu_1=mu_crand=0.5. Mu_min is different from this value, but it can be calculated analytically.
Hi,

All the coins are fair by assumption, so all the 's are 0.5.
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