Linear regression coefficients from covariance matrix
Standard error of regression coefficient without raw data
When can a sum and integral be interchanged? Let's say I have $\int_{0}^{\infty}\sum_{n = 0}^{\infty} f_{n}(x)\, dx$ with $f_{n}(x)$ being continuous functions. When can we interchange the integral and summation? Is $f_{n}(x) \geq 0$ for all $x$ and for all $n$ sufficient? How about when $\sum f_{n}(x)$ converges absolutely? If so why? Most efficient way to check for DBNull and then assign to a variable? How to change XML Attribute How can I change an attribute of an element in an XML file, using C#? "For someone used to the tiny creatures we get in England it was something of a shock."  I think, in this sentence, relative pronouns before some words have been omitted. I know rules of omitting relative pronouns, but in this case I have failed to understand before which words relative pronouns can be placed to understand the sentence perfectly, which has been stated above. Please, explain the rules of omitting relative pronouns with the help of the sentence stated above, so that I can be able to understand this type of sentences easily. You can also use other sentences to explain this fact clearly.  Thanks to everyone. I configured a journey in Marketing Cloud where i sent an email. My requirement is adding BCC email addresses to this email, but I noticed that we can only add valid email addresses. Could you confirm me that is not possible to add BCC /CC Address using personalization strings or Ampscript functions (e.g. Lookup) inside the Journey Email's settings? What's the equivalent of the "cls" command from Windows/DOS? Is there really no English equivalent to German's “Fachidiot”? There was the following paragraph in the article that came under the title, “GOP and the rise of Anti-knowledge” written by  (October 29, 2015):     “English unfortunately doesn’t have a precise word for the German   “Fachidiot,” a narrowly specialized person accomplished in his own   field but a blithering idiot outside it. In any case, a surgeon is   basically a skilled auto mechanic who is not bothered by the sight of   blood and palpitating organs. We need the surgeon’s skills on pain of   agonizing death, and reward him commensurately but that does not make   him a Voltaire.”    In Japanese we have a word, 専門バカ, of which literal translation is “specialist idiot” meaning exactly same as defined the above - a narrowly specialized person accomplished in his own field but a blithering idiot outside it.  I’m really curious about the absence of short descriptions of the specialist who knows nothing more than his specialty area in English like German “Fachidiot,” and Japanese "専門バカ."  Isn’t there really any short word counterpart to “Fachidiot,” specialist’s ignorance, for instance, in English?  P.S.  I found "narrow-minded specialisit" as a German-to-English translation of "fachidiot" in the web site, Interglot translation dictionary. So I have this word problem and I’m a bit confused about it. I have the answer and explanation but I still don’t understand: The half-life of carbon-14 is approximately 5730 years, while the half-life of carbon-12 is essentially infinite. If the ratio of carbon-14 to carbon-12 in a certain sample is 25% less than the normal ratio in nature, how old is the sample?     A. Less than 5730 years      B. Approximately 5730 years      C. Significantly greater than 5730 years, but less than 11460 years      D. Approximately 11460 years  Correct Answer: A Explanation: Because the half-life of carbon-12 is essentially infinite, a 25 percent decrease in the ratio of carbon-14 to carbon-12 means the same as a 25 percent decrease in the amount of carbon-14. If less than half of the carbon-14 has deteriorated, then less than one half-life has elapsed. Therefore, the sample is less than 5730 years old. Be careful with the wording here—the question states that the ratio is 25% less than the ratio in nature, not 25% of the ratio in nature, which would correspond to choice (D). How is the ratio of the carbon isotopes relevant to half-lives? What is the purpose of saying the half-life of an isotope is infinite? What is meant by “the normal ratio in nature”? Just based on the answer, it seems like the question said “25% of a carbon sample decayed, how old is this sample?” Obviously it’s younger than 5,730 years (the time for its first half life) because if only 25% decayed that means half a half-life has passed. I don’t see how isotopes and ratios would change this problem at all. Edit: Every answer here was very informative and helpful. It was tough to pick a best answer. I picked Cosma’s because it clicked with me. If you’re reading this and want to understand radiocarbon dating, look at every answer because there is some useful information in every answer Can I visit the US for tourism on a previously unused B1/B2 visa? Note: This is NOT a duplicate of  Difference: In both other questions, the posters traveled once to the US for the original purpose for which the B1 visa was obtained. Their question is about visiting again using the same visa. However, I've not traveled to the US yet, and I'm planning my visit. What I want to understand whether I can use this visa for a visit whose purpose is not the same as what was submitted along with the application.  Can I use a B1/B2 visa for tourism that was originally obtained for business purposes BEFORE I actually visit the US even once? I had applied for a business visitor visa for a valid business reason but by the time I got it stamped, my plan changed. So I've not visited the US even once. Can I now use this visa to visit as a tourist without having used that visa for its original intended purpose? PS: I live in India. Will  be supported on the Android App in the future? I visit A51 rather frequently and I would like to see it in the App. Let $P,Q$ real $n\times n$ matrices  such that $P^2=P$ , $Q^2=Q$ and $I-P-Q$ is an invertible matrix.  Prove that $P$ and $Q$ have the same rank.  Some help with this please , happy year and thanks. Big Greeks and commutation Writing a git post-receive hook to deal with a specific branch Is there a regular expression to detect a valid regular expression? Why do some lenses focus past infinity? On the kit 18-55 lens that came with my Nikon D5100 I have noticed that when trying to focus on infinity for shots in dark conditions (star-trails, etc) the lens tends to move past infinity out of focus and need to be brought back a little to get a clear infinity focus point.  Is there a good trick for getting a clear infinity focus when in pitch dark conditions? Where can I find web design projects? I am a recently graduated graphic designer. I would like to know if there are any worthwhile websites that I could present my portfolio and receive or look for job offers.  I have came across the following freelancewebsites by searching the web that seem to meet my criteria:       (the most famous website for people seeking for employers and employees)   I've also found two articles providing reviews on these types of sites:       I am new to the online freelance market. As a result, I don't have any clue which websites are mainstream for graphic designers and illustrators (which are my specialties). It's not immediately discernible to me which sites are the ones that are not a scam and are also good place for establishing myself.  I'm mainly looking for the resources that experienced designers are familiar with. I'm looking to narrow it down to the ones that have been used by those established in the industry. As a result I decided to consult the matter here and ask for input. Number of points on a line in a finite projective plane I've been reading some proofs regarding finite projective planes of order n, and often they start out by assuming that each line contains n+1 points. Is this a fact that follows from the axioms for finite projective planes? Or does this relate to the order of the finite field being projected? (for example in the Fano plane, does the fact that each line contains 3 points follow from the fact that there are 3 elements {0,1,2} in Z_2?) I haven't been able to find a clear explanation of this (clearly I do not yet have a solid understanding of how such planes are constructed). If someone could enlighten me that would be excellent. Defer Parsing of Scripts this is my first time to try this "Defer Parsing" thing, and I don't really have an idea how to do it.    Using PageSpeed tool, I found out that one of the reason why my page is loading too slow (currently 92/100) are the scripts. And the PageSpeed suggested that I need to Defer Parsing all those scripts.  Is there anyone that can help me with this. Thanks. I see the following error while trying run the command shown below. I read somewhere that my /boot partition is low on disk space. How can I increase the size of the /boot partition so I can install more software? I have a 500GB hard disk, so there is enough space to play with.  sudo apt-get install libdvdread4  gzip: stdout: No space left on device                                                                                                                                                                                  E: mkinitramfs failure cpio 141 gzip 1                                                                                                                                                                                 update-initramfs: failed for /boot/initrd.img-3.2.0-33-generic with 1.                                                                                                                                                 run-parts: /etc/kernel/postinst.d/initramfs-tools exited with return code 1                                                                                                                                            Failed to process /etc/kernel/postinst.d at /var/lib/dpkg/info/linux-image-3.2.0-33-generic.postinst line 1010.                                                                                                        dpkg: error processing linux-image-3.2.0-33-generic (--configure):                                                                                                                                                      subprocess installed post-installation script returned error exit status 2                                                                                                                                            dpkg: dependency problems prevent configuration of linux-image-server:                                                                                                                                                 linux-image-server depends on linux-image-3.2.0-33-generic; however:                                                                                                                                                    Package linux-image-3.2.0-33-generic is not configured yet.    dpkg: error processing linux-image-server (--configure):     dependency problems - leaving unconfigured    dpkg: dependency problems prevent configuration of linux-server:     linux-server depends on linux-image-server (= 3.2.0.33.36); however:      Package linux-image-server is not configured yet.    dpkg: error processing linux-server (--configure):     dependency problems - leaving unconfigured    No apport report written because the error message indicates its a followup error from a   previous failure.                                                                                                           No apport report written because the error message indicates its a followup error from a previous failure.  Errors were encountered while processing:  linux-image-3.2.0-33-generic  linux-image-server  linux-server N: Ignoring file 'michael-gruz-canon-precise.list.1' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension N: Ignoring file 'michael-gruz-canon-precise.list.1' in directory '/etc/apt/sources.list.d/' as it has an invalid filename extension   Listed below is the output of du  Filesystem              1K-blocks      Used Available Use% Mounted on /dev/mapper/ubuntu-root 712660664 104095912 572363692  16% / udev                      3964792         4   3964788   1% /dev tmpfs                     1591012      1064   1589948   1% /run none                         5120         0      5120   0% /run/lock none                      3977528       684   3976844   1% /run/shm /dev/sda1                  233191    219821       929 100% /boot I have a rather long footnote which breaks a listing in two parts, unnecessarily.  Since the listing is more important then the footnote I'd rather lake to have the footnote split.   Can I customize (one or all) footnotes to have a maximal length before they are continued on the next page? Or can I manually split a footnote in two to get the effect?