speed of the light emitted from a fast moving object
If I run along the aisle of a bus traveling at (almost) the speed of light, can I travel faster than the speed of light?
How should I take care of my new DSLR? I am getting a new Nikon D5100 (with 18-55mm VR Lens Kit). This is going to be my first DSLR. I wanted to get some tips from you guys on how to maintain it in the long term. I am getting a 52mm UV Protector Filter, as I read that it would do well to keep the lens clean.  Are there any precautions I need to take?  I would also appreciate if someone can suggest some reading material (paperback or online). I'm new to inequalities in mathematical induction and don't know how to proceed further. So far I was able to do this:  $V(1): 1≤1 \text{  true}$  $V(n): n!≤((n+1)/2)^n$  $V(n+1): (n+1)!≤((n+2)/2)^{(n+1)}$  and I've got : $(((n+1)/2)^n)\cdot(n+1)≤((n+2)/2)^{(n+1)}$ $((n+1)^n)n(n+1)≤((n+2)^n)((n/2)+1)$ I find I always have trouble scaling the amount of time the eggs should be boiled, cooled, etc. for different-sized batches of hard-boiled eggs.  I've heard a variety of "folk lore"-type rules for how it should be done, but what's really the right way? I am calculating the Intraclass Correlation coefficient (ICC) as per the method of Shrout-Fleiss (1979), using the (3, 1) model in which the judges are fixed as are the targets.  Some of my ICC values are negative.  Is this to be expected?  How to interpret this?  I understand that the maximum ICC is 1.0, but is there a minimum value?  How are negative values interpreted? I saw a lot of times claims that they have to be exhaustive (the examples in such books were always set in such way, that they were indeed), on the other hand I also saw a lot of times books stating they should be exclusive (for example $\mathrm{H}_{0}$ as $\mu_1=\mu_2$ and $\mathrm{H}_{1}$ as $\mu_1&gt;\mu_2$) without clarifying the exhaustive issue. Only before typing in this question I found somewhat stronger statement on the  -- "The alternative need not be the logical negation of the null hypothesis".  Could someone more experienced explain which is true, and I would be grateful for shedding some light on the (historical?) reasons for such difference (the books were written by statisticians after all, i.e. scientists, not philosophers). Recursively rename all the files without changing their extensions? How to recursively rename all the files in several layers of subdirectories without changing their extensions?  Below's a toned down version (to save room) of what I've got.  For argument's sake, I want all the files to have the same title, yet retain their original extension. There's never more than a single file per directory, so there's no chance of doubling up.  For simplicity, we'll just call them all foo, followed by their current extension.    So just to clarify: Asset\ 1.pdf, Asset\ 1.png, Asset\ 1@4x.png, Asset\ 1.svg Will become: foo.pdf, foo.png, foo.png, foo.svg And so on in that fashion.    I would typically use parameter expansion and a for loop, like:    for f in */*; do mv "$f" "${f%/*}/foo.${f##*.}"; done     But it's not recursive. So I would prefer to use something with find..-exec or similar.    ~/Desktop/Project/Graphics/ ├── Huge │   ├── PDF │   │   └── Asset\ 1.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── Asset\ 1.png │   │   └── 4x │   │       └── Asset\ 1@4x.png │   └── SVG │       └── Asset\ 1.svg ├── Large │   ├── PDF │   │   └── ProjectAsset\ 2.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 2.png │   │   └── 4x │   │       └── ProjectAsset\ 2@4x.png │   └── SVG │       └── ProjectAsset\ 2.svg ├── Medium │   ├── PDF │   │   └── ProjectAsset\ 3.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 3.png │   │   └── 4x │   │       └── ProjectAsset\ 3@4x.png │   └── SVG │       └── ProjectAsset\ 3.svg ├── Small │   ├── PDF │   │   └── ProjectAsset\ 4.pdf │   ├── PNG │   │   ├── 1x │   │   │   └── ProjectAsset\ 4.png │   │   └── 4x │   │       └── ProjectAsset\ 4@4x.png │   └── SVG │       └── ProjectAsset\ 4.svg └── Tiny     ├── PDF     │   └── Asset\ 5.pdf     ├── PNG     │   ├── 1x     │   │   └── Asset\ 5.png     │   └── 4x     │       └── Asset\ 5@4x.png     └── SVG         └── Asset\ 5.svg  30 directories, 20 files How to use combinatorial proof instead of induction? Let k ≥ 1 be an integer and consider a sequence $n_1, n_2, . . . , n_k$ of positive integers. Use a combinatorial proof to show that  $\binom{n_1}{2}$ + $\binom{n_2}{2}$ +...+ $\binom{n_k}{2}$ $\le$ $\binom{n_1 + n_2 + ...+ n_k}{2}$ Today is the release of Ubuntu 21.04 (Hirsute Hippo). And I can't update to this version. And also I selected ‘Notify me of a new Ubuntu version’ and changed it to ‘For any new version' on the Updates tab on Software &amp; Update, but it's still not working. In addition, in the terminal, I've written: sudo do-release-upgrade -c  And output was: Checking for a new Ubuntu release No new release found.  What should I do? Arduino only works in root I've installed Arduino but as the title says, I can only upload with sudo. And yes my user is part of the dialout group so that's the weird thing.   Arduino did function before on my system. What could be wrong?  Output ls -l:  ls -l /dev/ttyUSB* crw-rw-rw- 1 root dialout 188, 0 apr  2 09:23 /dev/ttyUSB0 Lightning component scripts loading issues since Spring 17 update I'm looking to do a third-party assessment of the false-positive rate of a video classification algorithm. Since I have a lot of video I'm trying to do a power analysis to figure out exactly how much video I need to look through so that it is representative of all the video data at a given confidence interval.  The algorithm flags video sequences that have at least one cat in it, and I'm looking to evaluate the frequency of false positives on a new unlabeled test set. So I have tagged all the video that my algorithm has identified a cat in and now want to sample the tagged video sections and look through them manually to validate my model since looking through all of it would take too long! Note, I'm not looking to refine the model at this point, just assess it.  My null hypothesis is that the FP rate of the sample of video I watch is equal to the FP rate of all the video.   I think I can use this formula to determine the number of video sequences to view:    Here is my question: am I thinking through this formulation correctly? Since my model has a CV false positive rate of ~0.96, I figure I can use that as a reference. Can I use that for the null hypothesis proportion, p0? Or will that be p, the true proportion?    I've been using this online calculator:   I ask because when setting the parameters I have, I'm getting very small sample sizes, like less than 10 sequences to view. That can't be right. Find the maximum likelihood estimator for $\theta$ when $f(x)=2\theta^{-2}x, 0\leq x \leq \theta$ Find the maximum likelihood estimator for $\theta$ when $f(x)=\frac{2x}{\theta^2}, 0\leq x \leq \theta$.  This should be a really easy question but I somehow cannot seem to get the right answer. My likelihood function is $\prod\limits_{i=1}^n \frac{2x_i}{\theta^2}$ which gives me after some simplification $n\ln(2\theta^{-2}) + \sum\limits_{i=1}^n ln(x_i)$ as my log-likelihood function. Then the derivative becomes $\frac{-2n}{\theta}$. If I equate this to $0$ to obtain the maximum I obtain $\hat{\theta}\rightarrow\infty$. However, this answer does not seem plausible. What did I do wrong? During kill Bill, we learn that all the black mamba had to do to get Hanzo to build her a sword, was to mention Bill's name.  When black mamba meets Bill at the end, she tells him that all she did was mention his name. Bill responds with, "that'll do it!"  So what was it that Bill did to Hanzo to make him come out of retirement and make another weapon of death? Change font of formula number in DisplayFormulaNumbered Existence of the moment generating function and variance Can a distribution with finite mean and infinite variance have a moment generating function? What about a distribution with finite mean and finite variance but infinite higher moments? How do I change the location of macOS screen captures? As a developer, I take a lot of screen captures. I often take screen shots to share with Stack Exchange members in chat.  The problem is my Desktop is so cluttered with screen captures that they're now overlapping! I'd like to save all screenshots in a dedicated folder or directory.  In macOS, how do I change the default location where screen captures are saved?  These are the screen shots taken with CommandShift3 or CommandShift4 keyboard shortcuts.  I would prefer a solution which doesn't require installing any software. Is there a way to substitute aliases such that it is appended or prepended to an existing command in the shell?   For example, defining the alias:  alias execloc='/home/user/'   Prepending this to a command in the bash terminal:  cd exeloc/temp/somefolder   Can something like this be done, or is there a way to do it? If we disbelieve $H_0$, why quote a p value calculated assuming $H_0$ was true? Hypothesis testing seeks to reject a null hypothesis ($H_0$) on the basis of an assumption made about the sample following a certain distribution. This assumption is conditional on $H_0$ being true. So what is the flaw with the following reasoning?     If I reject $H_0$ in favor of the alternative hypothesis ($H_1$), I   must then assume that (1) $H_1$ is true, and (2) that at the   same time the variable under examination follows the distribution   used to reject $H_0$. Since we also stated that the assumed   distribution is conditional on $H_0$ being true, it appears that $H_0$   has got to be true in order to justify the assumption made about the   distribution. Logically, it would therefore seem that both $H_0$ and   $H_1$ have to be true, which is a paradox, because they are mutually   exclusive! I have a query going that gets data for an ID for the last 3 months.  I need to tweak it so I get the highest value for each of the three months.  I've tried a couple of things with the aggregate function MAX, but I'm not getting anywhere.  I'm trying to get the max value for each of the past months ....  Here's the data from the query, currently sorted by date (asc):   ID      Date               Value 12410   01/03/2017 12:17    0.000178 12410   01/10/2017 11:36    0.000186 12410   01/17/2017 11:27    0.000189 12410   01/24/2017 13:09    0.000182 12410   01/31/2017 10:37    0.000169 12410   02/07/2017 11:03    0.000214 12410   02/14/2017 11:52    0.000176 12410   02/21/2017 10:51    0.000200 12410   02/28/2017 12:29    0.000194 12410   03/07/2017 08:39    0.000206   Here's the query:   select AnalysisID as "ID" , AnalysisDateTime as "Date", AnalysisValue as "Value" from AnalysisValueTbl where AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -3, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-3, getdate())) or AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -2, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-2, getdate())) or AnalysisID = 12410 and DatePart(m, AnalysisDateTime) = DatePart(m, DateAdd(m, -1, getdate())) and DatePart(yyyy, AnalysisDateTime) = DatePart(yyyy, DateAdd(m,-1, getdate())) order by AnalysisValue desc obtain a three-term asymptotic solution