I was wondering if creating "bullet gauges" is possible in any LaTeX package, but I didn´t find any.  In other question @Jake answered me with a solution for simple graphs in   I want to talk to somebody about this, because I think that it's a good contribution to LaTeX, and I'd like to invite to consider creating this kind of graphs as a new addition in the future, I think the use of this kind of graphs is increasing.  You can see bullet gauge original directives here, Stephen Few is the creator of this kind of graph:    Here you can see with more data:    In the version 9 of Mathematica, thee are a lot of options like you can see here:    I think that it may be useful reading data from files.
I am looking for a package to create bullet gauge graphs, but I couldn't find any.  A bullet graph looks like this:    and an ample description/specification can be found   It is available in Mathematica 9 ()  Is it possible create this kind of graphs in a easy way with TeX (like Matehmatica 9 or similar)?
Consistency of an order statistic in exponential distribution I have two questions.   1) If $X_1,X_2,X_3,...,X_n$ constitute a random sample of size $n$ from an exponential distribution, show that $\bar X$ is a consistent estimator of the parameter $\lambda$.    This is my attempt: Mean of exponential distribution is $\lambda^{-1}$. Thus by central Limit theorem $E(\bar X)=\lambda^{-1}$. Using mean square consistency, if  $\lim_{n\to \infty} E[(\bar X -\lambda )^2]=0$ then $\bar X $ is consistent for $\lambda$. Since $$ E[(\bar X -\lambda )^2]= E[(\bar X)^2]+E(\lambda)^2-2\lambda E(\bar X) , $$  I get $$ \lim_{n\to \infty} E[(\bar X -\lambda )^2] =    \lim_{n\to \infty} {2 \over \lambda ^2 }+\lambda^2-2 . $$ Clearly this is not equal to $0$. How can I show this is consistent? I tried using Chebechev inequality as well. But even using that I couldn't.    2) Is $X_{(n)}$ a consistent estimator for $\lambda$? If $P[|X_{(n)}-\lambda|&lt;\epsilon]$ approaches $1$ as $n$ goes to infinity for all $\epsilon &gt; 0$ then $X_n$ is a consistent estimator for $\lambda$.    The probability density function of $X_{(n)}$ is $f_n(x) = n \lambda e^{-\lambda x}(1-e^{-\lambda x})^{n-1}$,  for $X&gt;0$.  Thus \begin{align*} P[|X_{(n)}-\lambda|&lt;\epsilon]  &amp;= P[\lambda -\epsilon&lt;X_{n}&lt;\lambda+\epsilon] \\  &amp;=P[0&lt;X_{n}&lt;\lambda+\epsilon] \\  &amp;=\int_0^{\lambda+\epsilon} n \lambda e^{-\lambda x}(1-e^{-\lambda x})^{n-1}\\  &amp;= (1-e^{- \lambda X_{(n)} }), \end{align*} where $X{(n)}$ takes values in $[0 , \lambda+ \epsilon]$.  Thus, can I say $\lim_{n\to \infty}[1-e^{-\lambda(\lambda+\epsilon)}]^n=1$? How to make tr aware of non-ascii(unicode) characters? In the C and C++ programming languages, what is the difference between using angle brackets and using quotes in an include statement, as follows?   #include &lt;filename&gt;  #include "filename" I'd like to create a Categorized style in QGIS, classify with it data in a shapefile and then save the shapefile with the new categorized style. Is it possible? I have a situation very similar to the ones depicted in two previous questions I found ( and ), but still different (I address why my situation is different later on in the question).  The problem  I am really panicking, my computer has been in unbootable status for two days now and because of coronavirus lockdown, in Italy there is no any opened tech shop, at this point I do not know what to do and any help is very much appreciated.  I had a ~50 GB linux partition on the SSD (total ~250 GB) of my 15” Macbook Pro mid-2015. I created this partition to boot ubuntu back in 2016 and I used it regularly alongside macOS. About one year ago I updated to Mojave 10.14, and this is the macOS version my computer is running now (I am mentioning it because I suppose that the update changed the file system of my macOS partition to APFS, keeping unmodified the ubuntu partition, I guess).  Today I decided to remove the ubuntu partition, I started the computer on macOS, opened Disk Utility, find the ~50 GB partition assigned to ubuntu on the pie chart, I clicked on the “-“ sign to remove the partition and then “Apply”. Disk Utility returned to me instantly with an error (not remember exactly the text, but I remember that no error code was given) saying it could not perform the operation, so I googled a bit some solutions (MY COMPUTER WAS PERFECTLY WORKING) and I found a post suggesting to perform some operations from ubuntu, so I decided to restart my computer in order to open ubuntu - I repeat, it was perfectly working, many apps opened and fully working, etc. - and...  It booted into “GNU GRUB version 2.02”  I tried to restart my mac keeping “option” pressed, but it could only find the “EFI Boot” disk (picture attached) which is the one I usually select to boot Ubuntu. Also, Ubuntu now doesn’t even work anymore, because if I select “EFI Boot” it starts “GNU GRUB version 2.02”.  Now I really started panicking, I don’t care about data of the ~50 GB ubuntu partition, but so foolishly I haven’t backed up the ~200 GB macOS data, and I am just so affectionate to them, I would really like to recover them.  Data Recap   15” Macbook Pro mid-2015 Right now I am booting from the network. 256 GB SSD partitioned in: ~200 GB APFS macOS partition - FileVault encrypted - running Mojave 10.14 ~50 GB ubuntu partition - don’t remember the file system (data here doesm’t matter to me)   Photos Attached   diskutil list gpt -r show /dev/disk1 disk1 information from Disk Utility Disk Utility overview of the physical disk booting situation with only the “EFI Boot” partition   Why my situation is different  My situation is different from other questions because of 3 reasons:   The ~50 GB ubuntu partition is disappeared, maybe corrupted, indeed if you add up all the disk's size in diskutil list, you still miss ~50 GB. I have 2 disks at the same time (index 2 and index 3) that are in the FFFFFFFF-FFFF-FFFF-FFFF-FFFFFFFFFFFF status When I call gpt -r show /dev/disk1 I don't get any "Suspicious MBR at sector 0" message unlike others users that wrote other questions.   Update 1  I just wanted to confirm that I am booting the mac from Network Recovery and also my Disk Utility version. Disk Utility Version is: "Version 13 (606)" - "Copyright 2002-2014 Apple Inc.". Is seems, indeed, pretty old. Cross product: matrix transformation identity How can one prove the following identity of the cross product?  $$(M a)\times (M b)=\det(M) (M^{\rm T})^{-1}(a\times b)$$  $a$ and $b$ are 3-vectors, and $M$ is an invertible real $3 \times 3$ matrix. Is there a page listing all fields? Why girth of Petersen Graph is five? (Proof) I want to know, what is the mathematical proof that shows the shortest cycle in Petersen Graph has length five? Reapplying for a UK Standard Visitor visa after a refusal Prove that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw) \subset \mathbb{A}^4$, is not a unique factorization domain I want to show that $k[x,y,z,w]/(xy-zw)$, the coordinate ring of $V(xy-zw)\subset\mathbb{A}^4$, is not a unique factorization domain.    Morally, all we need to do is find some nonzero element that can be written in two distinct ways as a product of irreducible elements, but nothing is coming to mind immediately. Thoughts? Two column float with [t] using the cas-dc template I am using the cas-dc template for Elsevier. When trying to use \begin{figure*}[t], except I get the error 'The module 'cas/fig' does not have a key called 'cas/fig/t'. Other templates I use work fine. I have included \usepackage{stfloats}. I don't see anything mentioned that strictly forbids it, unless I missed this. Anyone know why? Does a photon exert a gravitational pull? Adding coordinate system to layout in QGIS composer? I would like to know if there is a way to add a dynamic coordinate system field into a QGIS composer layout.  I can use an expression to add many items such as document name, file path, etc but I can;t seem to figure out how to add the coordinate system? The question asks it all really. When referring to a master's degree, do you use an apostrophe or not? That is, is it "a master's" or "a masters"? How can I find all files I can not write to?  Would be good if it takes standard permissions and acls into account.  Is there an "easy" way or do I have to parse the permissions myself? What methods can I use to create balance and consistency between a group of differing logos? A regular challenge that I face is balancing two (or more) logos. Whether they need to be equal or one needs to be given priority. Some logos however might be squares, others rectangles, circles, etc...   As a quick sample I snagged a nice high resolution photo from  and pretend its going to be an advertisement that needs to show some footwear brand logos on it. In this case I used Adidas and Saucony.  This is certainly not balanced even though they're height is the same:    Likewise this is not balanced even though they're width is the same:    So then the question becomes when are they in balance, is this balance:    Maybe a little more adjustment, is this balance:    And in these examples I'm only working with two Black Logos. Factor in color and it can get even more difficult to balance. Another issue being when there's tiny text as part of the logo.  So the question is, other than estimating / eye-balling it, what tips, methods or even tools are there to balance different sized logos? How to Deserialize XML document Here's a module with castellated pads attached to an eval board:  (source: ) Looking closely at the wires interfacing with the castellated pads, they're clearly soldered to the eval board. However, they don't look like they're soldered to the module, but rather they're being pressed against the pads with the tension in the wire. It also looks like the free end of the loops are protruding down into a channel cut in the PCB. Do these kind of connectors/metal loops have a name? Are $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ different? I have seen the claim that $T\mathbb{S}^2$ and $\mathbb{S}^2 \times \mathbb{R}^2$ are not diffeomorphic, but I have only ever seen the proof that they are not isomorphic as vector bundles (which is a cute application of the hairy ball theorem). How would I prove that they are indeed not diffeomorphic (or better, not homeomorphic)? Update manager doesn't offer an upgrade to the new release