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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
Aug
7
answered How to find eigenvalues of matrix $\begin{bmatrix} 3& a+1\\a+1&3 \end{bmatrix}$
Aug
7
accepted Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
Aug
7
comment Why does $[X\in A]=[(X, Y)\in A\times \mathbb R]$
@Berci It appears that other answers are not consistent with your comment (see discussion under Augustin's answer), would you like to elaborate or change it?