Hi Professor,

I just have a hard time to understand that how choosing a hypothesis changes a theory -- Hoeffding inequality.

Let's say h1(x) < P1, h2(x) < P2. We choose h2 to be g. Then h2(x) < P2 is no longer true?

I sort of understand your example because we pick the run of coin flipping that produces most heads, and so if we plot the graph, the graph indicates that Hoeffding inequality doesn't apply. But Hoeffding inequality is talking about probability and so the reality might be off a bit.

Maybe I am in a wrong direction?