Well-posed vs. well posed
When should com­pound words be writ­ten as one word, with hy­phens, or with spaces?
I need to calculate the Cramer Rao lower bound of variance for the parameter $\theta$ of the distribution $$f(x)=\frac{1}{\pi(1+(x-\theta)^2)}$$   How do I proceed I have calculated $$4 E\frac{(X-\theta)^2}{1+X^2+\theta^2-2X\theta}$$  Can somebody help I have recently a purchased Lenovo Thinkpad E480 laptop, I have installed Ubuntu 18.04 on it, everything is working fine except am not able to connect to network via WiFi. Please help.  I followed this , but am unable to solve the issue.  Below are the outputs of some commands.  lsb_release -a  No LSB modules are available. Distributor ID: Ubuntu Description:    Ubuntu 18.04.1 LTS Release:    18.04 Codename:   bionic   uname -r  4.15.0-33-generic   rfkill list all  0: tpacpi_bluetooth_sw: Bluetooth     Soft blocked: no     Hard blocked: no 1: hci0: Bluetooth     Soft blocked: no     Hard blocked: no   lspci -nnk | grep 0280 -A3  05:00.0 Network controller [0280]: Realtek Semiconductor Co., Ltd. RTL8821CE 802.11ac PCIe Wireless Network Adapter [10ec:c821]     Subsystem: Lenovo RTL8821CE 802.11ac PCIe Wireless Network Adapter [17aa:c024] 06:00.0 SD Host controller [0805]: O2 Micro, Inc. SD/MMC Card Reader Controller [1217:8621] (rev 01)     Subsystem: Lenovo SD/MMC Card Reader Controller [17aa:5068]   sudo lshw -C network   *-network                         description: Ethernet interface        product: RTL8111/8168/8411 PCI Express Gigabit Ethernet Controller        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:03:00.0        logical name: enp3s0        version: 10        serial: 8c:16:45:a3:d9:f1        size: 100Mbit/s        capacity: 1Gbit/s        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress msix vpd bus_master cap_list ethernet physical tp mii 10bt 10bt-fd 100bt 100bt-fd 1000bt 1000bt-fd autonegotiation        configuration: autonegotiation=on broadcast=yes driver=r8169 driverversion=2.3LK-NAPI duplex=full firmware=rtl8168g-3_0.0.1 04/23/13 ip=192.168.2.2 latency=0 link=yes multicast=yes port=MII speed=100Mbit/s        resources: irq:16 ioport:d000(size=256) memory:f1204000-f1204fff memory:f1200000-f1203fff   *-network UNCLAIMED        description: Network controller        product: Realtek Semiconductor Co., Ltd.        vendor: Realtek Semiconductor Co., Ltd.        physical id: 0        bus info: pci@0000:05:00.0        version: 00        width: 64 bits        clock: 33MHz        capabilities: pm msi pciexpress cap_list        configuration: latency=0        resources: ioport:c000(size=256) memory:f1100000-f110ffff   It seems I have to clone, compile and install the required WiFi driver, please guide me which WiFi driver to use and how to install (with steps if possible).  P.S.: Let me know if any further information is needed to solve this issue, I will add the required info (if any) in the question as per the guidance given. I wanted a simple environment for making lists of equations, so I made one that includes an equation and a split environment. The code won't compile and the error seems unrelated. The most pressing thing I noticed was the &quot;You can't use `\end' in internal vertical mode.&quot; The problem is definitely the split environment. Here is a MWE. \documentclass{article} \usepackage{amsmath}  \newenvironment{env}     {\begin{equation}\begin{split}}     {\end{split}\end{equation}}  \begin{document} \begin{env}     x \end{env} \end{document}  If I remove the split environment from env, everything compiles just fine. Additionally, If the following example compiles just fine. What is the problem then? \documentclass{article} \usepackage{amsmath}  \begin{document} \begin{equation} \begin{split}     x \end{split} \end{equation} \end{document}  Here is the LaTeX error upon running the MWE. math.tex|11 error| LaTeX Error: \begin{split} on input line 9 ended by \end{env}. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing \cr inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Missing { inserted. math.tex|12 error| Extra }, or forgotten $. math.tex|12 error| Missing $ inserted. math.tex|12 error| Missing } inserted. math.tex|12 error| You can't use `\end' in internal vertical mode. math.tex|12 error| LaTeX Error: \begin{equation} on input line 9 ended by \end{document}. math.tex|12 error| Missing } inserted. math.tex|12 error| Missing $ inserted. math.tex|12 error| Display math should end with $$. math.tex|| Emergency stop. math.tex|| ==&gt; Fatal error occurred, no output PDF file produced! Showing that every field is an integral domain. Sum with parameter convergence How can I easily switch audio output in Ubuntu 17.10 and later with GNOME? What is the terminology for data aggregated via summed totals versus data aggregated via means? The two types of data differ in that if you decide to decrease the temporal (time) resolution of the first type of data you take the mean of lower the resolutions. With the second you take the sum over the lower resolutions. Here is a concrete example  Gas Used (kWh), Outside Air Temperature (C), Time Resolution (Minutes) 100, 20, 20 140, 22, 20 120, 21, 20   Here the hourly (60 Minute) resolution data is clearly  360, 21, 60   and is found by averaging the temperature and summing up the gas used.  What I really wish to know is what the names for each of these types of data are called. I understand that this question is not the best but it is hard to ask a question about something whose names you do not know. If you have a better way of articulating the question then please go ahead and edit it. What is the difference between these two Breusch-Pagan Tests? Using R on some data and trying to see whether or not my data is heteroscedastic, I've found two implementations of the Breusch-Pagan test,  (package lmtest) and  (package car). However, these produce different results. What is the difference between the two? When should you choose to use one or the other?  &gt; model &lt;- lm(y ~ x) &gt; bp &lt;- bptest(model) &gt; bp studentized Breusch-Pagan test  data:  model  BP = 3.3596, df = 1, p-value = 0.06681  &gt; ncvTest(model) Non-constant Variance Score Test  Variance formula: ~ fitted.values  Chisquare = 3.858704    Df = 1     p = 0.04948855    These example shows that according to the tests, my data is in one case heteroscedastic and in the other case homoscedastic. I did find  so bptest might be studentized and ncvTest might not be, however, what does this mean then? Determining Min - Max within zip code (statistics by area)? I'm new to ArcGIS Desktop. I have created a layer representing zip codes and overlayed it with a layer containing some data points. I want to find the min and max value of the data points in each zip code. Currently, I am manually checking the values if all the data points in each zip code but this is becoming very time-consuming and cumbersome.   Is there a faster way to do this? Graph Proof by induction. Can you prove via induction that there exists a node in a directed graph of n nodes that can be reached in at most two edges from every other node in the graph. Every node in the graph is required to have an edge with every other node that either points out or in (For every pair of nodes X and Y, either X points to Y or Y points to X). How to quickly and easily create a grid with Adobe Photoshop? Suppose I need to draw a grid in Photoshop, each square being the same size, and a certain amount of pixels tall and wide, and the grid lines having a certain pixel width. Like this:     Currently I do this by drawing one square, copy+pasting+moving+merging it a few times to create one row, copy/pasting that a few times to create more rows above each other.  It works, but feels very clumsy, I'm sure there ought to be a more efficient way to do this?  What are some efficient methods for creating a grid of equally sized squares? This post is an expansion of  For many graduated sites (eg Physics), moderators do not want to apply the unilateral close vote in all cases--it is better to let some community votes pile on first.  We only use the unilateral in obvious cases then. This renders the CV queue useless to us. If we &quot;skip&quot; something, we can't get back to it. If we say &quot;do not close&quot;, it's removed from the queue and our community can't see it. If we use &quot;close&quot;, we are using a unilateral mod vote--we don't want to do that. What I propose is a set of &quot;next/previous&quot; buttons, that let us navigate the queues, looking for closeable questions, and coming back to the others later. Thoughts? Update and bounty reason Due to the recent Great Flag Overhaul, mods no longer see close flags in the flag queue. Which means that the only way to get to them is via the review queue 1 Shog's solution is ideal in this case; let mods view the close queue as a list. (In fact, a list similar to the old flag queue -- which shows a list of mods who have seen the post and what mod actions have already been taken -- would be great) On Physics, the majority of the flags that we get are VTC flags. And the community isn't always able to close things on their own, so we have to step in. However, powering through the close queue isn't an option; because &quot;skip&quot;ing a post2 leads to it being dumped into the void (I can't get back to it unless I have a link). Extremely inconvenient. Could the workflow here be improved? 1. The /tools listing for posts with outstanding close votes doesn't work because it doesn't list posts which have been flagged but not VTCd 2. which I may want to take a closer look at later; gotta be careful with the binding votes. How do you add a timer to a C# console application Just this - How do you add a timer to a C# console application? It would be great if you could supply some example coding. Evaluation of $\lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}n^n}$ without stirling approximation Evaluation of $\displaystyle \lim_{n\rightarrow \infty}\frac{n!\cdot e^n}{\sqrt{n}\cdot n^n}$   $\bf{My\; Try::}$we can write it as $$l=\lim_{n\rightarrow \infty}\frac{e^n}{\sqrt{n}}\cdot \left(\frac{1}{n}\cdot \frac{2}{n}\cdot \frac{3}{n}\cdots \cdots \frac{n}{n}\right)$$  $$\ln (l) = \lim_{n\rightarrow \infty}\bigg[n-\frac{1}{2}n+\sum^{n}_{r=1}\ln\left(\frac{r}{n}\right)\bigg]$$  Now how can i solve it, Help required, Thanks Every countably generated sigma algebra is generated by a random variable I've seen many of the solutions on the topic, all posted in this site. But I haven't seen any of them mentioning Apple's adapter,   I have that, which was used to connect to my old MacBook Pro 2013.   Now, I'm assuming that all I need is to connect the Mini DisplayPort to an adapter, such as  (as mentioned in one of the posts) and the USB cable to a USB-C adaptor.   Is this correct? If $\sum_{n_0}^{\infty} a_n$ diverges prove that $\sum_{n_0}^{\infty} \frac{a_n}{a_1+a_2+...+a_n} = +\infty $ I've tried to use the limit test: $\lim_{n \rightarrow \infty} \frac{a_n}{b_n} = C$ in the series of $a_n$ and $\frac{a_n}{a_1+a_2+...+a_n}$ but it was inconclusive.  The question does not especify the sign of $a_n$ but proving it for positives would already help.  I think the sign can change as long as the partial sums never get to be zero. Like if the series has only negative numbers the result seems to stil hold. Wouldn't the thermodynamic cost of creating alternate universes make the Many Worlds interpretation implausible? I was thinking about the many interpretations of quantum physics, and one thing that never made sense to me was the many world's interpretation. Basically at any given moment for which something exists in a superposition, isn't this interpretation basically saying that there would have to exist a new universe for every possible discrete outcome that could result once the measurement is made?   So let's say an electron's location is a superposition of two distinct locations. Doesn't that mean there would at that moment have to be two distinct universes for each distinct location that is superposed? If so, then clearly the amount of universes being spawned every moment must be astronomical.   There could be trillions upon trillions of electrons(for instance) having superposed states, and then every moment in time (I suppose every planck time?), it seems there would have to be yet another set of universes spawning for every superposition.  How could this be? Surely there must be some kind of thermodynamic cost to replicate an entire universe. What would fuel or supply the additional mass and energy for every universe at every moment for every superposed state?  To my lay person's mind, this seems to be a very big weakness of this interpretation, but I needed to ask people with the physics background required to answer this question. Could there be some kind of loophole that could allow alternate universes to spawn so rapidly? Otherwise, doesn't this present a bit of a problem for taking this interpretation seriously? How to determine a Python variable's type? How do I see the type of a variable whether it is unsigned 32 bit, signed 16 bit, etc.?  How do I view it? I sometimes get files from my clients that have the wrong file extension. For example, the name is image.jpg but the file is actually a TIFF image. In many cases I can clarify it by opening the file in a text editor, looking at the first few bytes, then deducing which file type it is.  This works for me with JPEG, TIFF, GIF and PDF files. However there are many more file types out there.  Is it possible to automate identification of the correct file type by analyzing the containing data?