Quote:
Originally Posted by yaser
Your answers to (a) and (c) are both correct. They are not in conflict since (a) is asking a deterministic question while (c) is asking a probabilistic question.

For part c, I thought:
Given p = 0.9, h1 is a better hypothesis than h2.
Hence, the probability that S produces a better hypothesis than C is the probability that S picks h1 essentially as C will pick the other hypothesis that S doesn't pick.
In other words, P[S produces a better hypothesis than C] = P[S picks h1 based on the 25 training examples].
S will pick h1 if 13 out of 25 training examples give +1, so we will have:
P[S picks h1]
= P[13 or more out of 25 training examples give +1]
=
= 0.9999998379165839813935344
It is quite different from tatung2112's explanation for c.
Could you comment further?
Thanks!