#1




Page 63 and excercise 2.8
On page 63 its given that g_(x) is approximately the mean of all gk(x) for any x. Why is it an estimate and not exactly the mean?
Since g_(x) is the average for any x, then its possible for it to have non binary values for a binary classification problem. But this seems to be a bit counter intuitive to me. Can you please clarify if my understanding of g_(x) is correct 
#2




Re: Page 63 and excercise 2.8

#3




Re: Page 63 and excercise 2.8
because is defined as an expectation with respect to data sets of g(x). The average over data sets approximates this expectation.
Yes, is not a valid hypothesis: it may not be in your hypothesis set; it may not even be binary. It is never used as a classifier. It is just used to represent "what would happen on average after learning", and this abstract function plays a role in defining the bias in the bias variance decomposition.
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Have faith in probability 
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