#11




Re: Q1 and Q2
I will rephrase 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




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




Re: Q1 and Q2
Quote:
For me it does , read closely : νmin is closest to: 
#14




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




Re: Q1 and Q2
Quote:
All the coins are fair by assumption, so all the 's are 0.5.
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