[alinsoar]

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 ?