Quantum Mechanics - How do we know that the observed locations of electrons are random?
How do we know that certain quantum effects are random?
Left ideals of $M_n(K)$ What are the reputation requirements for privileges on sites, and how do they differ per site? Formerly Reputation requirements compared. What are the reputation requirements for privileges on the various sites in the network? Also, how do reputation requirements for various privileges compare on different Stack Exchange sites? Specifically, the following types of sites:  Designed sites e.g. Stack Overflow, Ask Ubuntu, Gaming, etc. Public beta and non-designed sites Private beta sites  ...as well as any site-specific differences. Typeset the shrug ¯\_(ツ)_/¯ emoji I'm completing a problem set, one problem for which I literally have no idea what to do on. The graders would prefer to have a physical copy of the problem so I thought it best to include the ¯\_(ツ)_/¯ emoji as my answer, instead of something like "Dunno" or "No idea."  Option #1 is to include an image.  Beyond that I actually don't understand how this emoji works. The middle character is Japanese kana "tsu" and proves problematic - TeX wants it in math mode then renders "?" when it is. What is a one-word synonym for "science lover"? I'm searching for a one-word synonym for "science lover". In my case, I love science and I self study it, but I never got a degree in Physics or Chemistry or any of these related subjects (except computer-science). But I enjoy experimenting stuff and see what's going on.  So, what would be a one-word good alternative for "science lover"?  The best one I found is learner, but that's more general I guess. Scientist is probably too much in my case. I saw sciencophile in another post, but I don't really like it–it sounds too complicated. Gendry was born in the Crownlands and should therefore be referred to as Gendry Waters. However, he refers to himself as Gendry Rivers.   Did showrunners forget or is Gendry ignorant of the customs? If you visit a chat room attached to a beta site while logged out, the log in message is all but unreadable, being dark grey on a dark blue background. For example, visit  while logged out or in private browsing mode. How do I save files edited with vim? How to refresh the specific Lightning component not the lightning page I have two lightning component placed on one page lightning app. First Component have refresh icon and I set onclick action to refresh Component $A.get('e.force:refreshView').fire(); but this event refresh the whole page instead of First component.  how can refresh only one component on page not all the page ? Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ Let $A,B,C$ be sets, and $B \cap C=\emptyset$. Show $|A^{B \cup C}|=|A^B \times A^C|$ by defining a bijection $f:A^{B \cup C} \rightarrow A^B \times A^C$.  Any hints on this one?  Thank you! Regular cast vs. static_cast vs. dynamic_cast I've been writing C and C++ code for almost twenty years, but there's one aspect of these languages that I've never really understood. I've obviously used regular casts i.e.  MyClass *m = (MyClass *)ptr;   all over the place, but there seem to be two other types of casts, and I don't know the difference. What's the difference between the following lines of code?  MyClass *m = (MyClass *)ptr; MyClass *m = static_cast&lt;MyClass *&gt;(ptr); MyClass *m = dynamic_cast&lt;MyClass *&gt;(ptr); What screenshot tools are available? I have noticed that many people use images in their Ask Ubuntu answers. What software are people using? Paying off student loan or using that money for a downpayment on a house How do I delete one of two Ubuntus on my PC How to check that a cubic polynomial is irreducible? I want to argue that argue that $\pi(\alpha)=\alpha^3+3\alpha+3$ is an irreducible polynomial over the finite field with 5 elements $\mathbb{F}_5$. My approach was just to check that $\pi$ has no roots in $\mathbb{F}_5$. Is this right? "How big of a problem" vs. "how big a problem" Quite a few phrases in English are constructed like so:     How [adjective] a [noun]...?   This is the question form of the construction, which is often answered with the negative:     Not that [adjective] a [noun].   or the positive:     Quite [adjective] a [noun].   However, from time to time I'll hear the word 'of' inserted before the 'a', e.g.:     Not that [adjective] of a [noun].   This usually sounds wrong to me, with the exception of the case where the adjective 'much' is used.  So, this sounds fine to my ear:     Not that much of a problem.   whereas this doesn't:     Not that loud of a noise.   Why is it that 'much' should be used with 'of', and other adjectives not?  Is it because 'much' is seen as measuring a quantity (of something), whereas other adjectives that may be used in this construction are seen as measuring the quality of a whole thing? I've looked at the resumes of the type of candidates that get into computer science PhD programs at the top few universities (e.g. Stanford, MIT etc.) and a lot of them seem to have multiple publications (2-4) done during their undergraduate years. Is this representative of the entire pool? Or is this just a self-selected group that puts their resumes online.  I currently have one first-author workshop paper (5 pages), and I wonder how this might affect my chances at entry into these top universities. I am currently reading Murphy's ML: A Probabilistic Perspective. In CH 3 he explains that a batch update of the posterior is equivalent to a sequential update of the posterior, and I am trying to understand this in the context of his example.  Suppose $D_a$ and $D_b$ are two data sets and $\theta$ is the parameter to our model. We are trying to update the posterior $P(\theta \mid D_a, D_b)$. In a sequential update, he states that, $$ (1) \ \ \ \ \ \ \ \  P(\theta \mid D_{a}, D_{b}) \propto P(D_b \mid \theta) P(\theta \mid D_a) $$ However, I am slightly confused as to how he got this mathematically. Conceptually, I understand that he is saying the posterior $P(\theta \mid D_a)$ is now a prior used to update the new posterior, which includes the new data $D_b$, and is multiplying this prior with the likelihood $P(D_b \mid \theta)$. Expanding the last statement out, I have, $$  P(D_b \mid \theta) P(\theta \mid D_a) = P(D_b \mid \theta) P(D_a \mid \theta) P(\theta) $$  but are we allowed to say $P(D_a \mid \theta) P(D_b \mid \theta) = P(D_a, D_b \mid \theta)$ in order to make the connection in (1)? When should I use exposure compensation? When should I use exposure compensation, rather than ISO, shutter speed or aperture? Is radioactive decay spontaneous or random? When it comes to radioactive decay, what is the difference between random and spontaneous?  For example, when the count rate of a radioactive isotope is measured, the readings fluctuate. Is this a demonstration of the randomness of the process, or of its spontaneous nature? Q&A blank in Stack Exchange Android app v1.0.95 - S10e/Android 10 Recently upgraded to a Samsung S10e and Android 10, but all Q&amp;A in the Stack Exchange app v1.0.95 are blank.  The title and comments are visible, but question/answer posts are just white space. Accessing the About page in the app is also blank.  I tried clearing data, cache and re-installing the app, but I still get the same behaviour.