[Script Info]
Title:
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:00.70,0:00:09.90,Default,,0000,0000,0000,,Now, the first answer is two-third, and the reason is we observed A once, and this was all we observed.
Dialogue: 0,0:00:09.90,0:00:13.67,Default,,0000,0000,0000,,So maximum life would give us a probability of one, but because we used Laplacian smoothing,
Dialogue: 0,0:00:13.67,0:00:19.07,Default,,0000,0000,0000,,and there's two different possible states, we add one, as before, which makes two-thirds.
Dialogue: 0,0:00:19.07,0:00:28.63,Default,,0000,0000,0000,,Two-thirds is also the correct answer for the next question. There's one, two, three, four transitions out of A,
Dialogue: 0,0:00:28.63,0:00:37.30,Default,,0000,0000,0000,,three of which leads to A again. So maximum life would give us three-quarters, but because we do Laplacian smoothing,
Dialogue: 0,0:00:37.30,0:00:42.100,Default,,0000,0000,0000,,we add one fake transition over here, and there could've been two of those, one to A and one to B, we had two over here,
Dialogue: 0,0:00:43.00,0:00:49.63,Default,,0000,0000,0000,,which is four over six or two over three. And there's no transition out of B in this example.
Dialogue: 0,0:00:49.63,0:00:57.20,Default,,0000,0000,0000,,So for maximum life we wouldn't even know what to say. But in our case, with Laplacian smoothing, we add one fake observation
Dialogue: 0,0:00:57.20,0:01:01.67,Default,,0000,0000,0000,,divided by two as a denominator, so we get half for the last question.