Dahn Jahn
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 Oct 25 comment Strong and weak extrema I upvoted the other answer and accepted my own. Not sure if my answer is the one that made me understand, because (surprisingly) I wrote it after understanding the problem, but I feel like this explanation (albeit very similar) would help me more. Oct 25 accepted Strong and weak extrema Oct 25 asked Proving Independence Intuitively Oct 25 comment the probability that there's an actual tornado if the alarm goes off (discrete math) Yes. If the test correctly diagnoses the disease in 99% of times it is still entirely possible that you have less than 1% chance of having the disease, depending on how rare it actually it (which makes the false positives much more common). Also it makes you aware of how different $P(A|B)$ and $P(B|A)$ can be, which is something non-mathematicians often confuse. Oct 25 comment the probability that there's an actual tornado if the alarm goes off (discrete math) You're welcome. Bayes theorem is arguably one of the most amazing things you will probably encounter in an introductory probability lessons not based on measure theory (which I am guessing is your case), so I highly recommend actually understanding it. If you ever get a positive result for a scary disease, you'll thank your understanding of math and calm down a bit :) Oct 25 revised the probability that there's an actual tornado if the alarm goes off (discrete math) More precise link Oct 25 answered the probability that there's an actual tornado if the alarm goes off (discrete math) Oct 20 comment Shift-invariant Sets Are Terminal Sets Oh my god, it is true! This semi-blows my mind. At the same time I really dislike the fact that I would never realize it wouldn't being (repeatedly) told it is so. Oct 20 accepted Shift-invariant Sets Are Terminal Sets Oct 20 comment Shift-invariant Sets Are Terminal Sets How do we know that $s^k x \in I$? It's not readily available from the definition of a shift-invariant set. Oct 20 asked Shift-invariant Sets Are Terminal Sets Oct 16 accepted Geometric Interpretation of the Separation Theorem Oct 16 awarded Good Question Oct 14 revised Geometric Interpretation of the Separation Theorem added the geometric interpretation Oct 14 comment Geometric Interpretation of the Separation Theorem True, will add. Oct 14 revised Geometric Interpretation of the Separation Theorem added 6 characters in body Oct 14 asked Geometric Interpretation of the Separation Theorem Oct 12 answered Strong and weak extrema Aug 13 comment Interpretation of $\sigma$-algebra and filtrations (follow-up question) Thank you for answering an older question, it's always a bit frustrating to get no answers. Since posting this question, my understanding of probability has (luckily) expanded, so this all makes much more sense now. And yeah, the non-constructiveness of the conditional expectations keeps bugging me again and again, looking forward to the day when I'll be able to say that I "got it". Aug 10 revised How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$ deleted 1 character in body