section 3.13 on the deeplearningbook says
A message saying “the sun rose this morning” is so uninformative as to be unnecessary to send, but a message saying “there was a solar eclipse this morning” is very informative.
the self-information of an event $X=x$ is in this form
$I(x) = -\log P(x)$
assume a solar eclipse is not predictable and there are N days when there was a solar eclipse, in the 100 years between 1900 to 2000.
the self-information of “there will be a solar eclipse tomorrow morning” is approximately equal to
$-\log \frac{N}{365*100}$
am I doing this correctly?