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What does capital letter I mean in this formulas? Hello I don't understand meaning of the symbol represented by a capital letter "I" in the formulas below. There is  to the paper with the formulas.    At the beginning I thought it mean "where c is not equal to the result of classifier T(m)", however in step (d) there is a multiplication symbol before it, so it probably mean that "I" should "return" a value. Symbolizing using RGB values from Excel in ArcGIS Desktop? I have an excel file with 2 attribute columns, 1-feature info 2-Number of color (RGB) that the current feature should be symbolize. This file file can be joined with the layer using the "feature info" field which is unique (join by attribute table). So i have as attribute the color number attribute for every polygon feature.  How can  i use this this information to symbolize every feature with their attributed color already imported from the excel sheet? $E|X-m|$ is minimised at $m$=median For a continuous random variable $X$, I want to show that $E|X-m|$ is minimum implies $m$ is the median of the distribution. Assume that the distribution function is $F$ and the density function is $f$.  In this case, we basically need to minimize  $$\int_x |x-m|f(x)\,dx=\int_{x&gt;m}(x-m)f(x)\,dx+\int_{x&lt;m}(m-x)f(x)\,dx.$$  I am finally being left with $2mF(m)-m+E(X)-2\int_{x&lt;m}xf(x)\,dx$. What does it mean to minimise this expression? Is there some way out?  Well, my intuition says that since I have to prove that $F(m)=0.5$, I somehow will need to show that $E|X-m|$ is minimised if $2mF(m)-m=0$ (as then I will get $F(m)=0.5$ Coupon collector's problem: mean and variance in number of coupons to be collected to complete a set (unequal probabilities) There are $n$ coupons in a collection. A collector has the ability to purchase a coupon, but can't choose the coupon he purchases. Instead, the coupon is revealed to be coupon $i$ with probability $p_i=\frac 1 n$. Let $N$ be the number of coupons he'll need to collect before he has at least one coupon of each type. Find the expected value and variance of $N$. Bonus: generalize to the case where the probability of collecting the $j$th coupon is $p_j$ with $\sum\limits_{j=1}^n p_j=1$  I recently came across this problem and came up with/ unearthed various methods to solve it. I'm intending this page as a wiki with various solutions. I'll be posting all the solutions I'm aware of (4 so far) over time.    EDIT: As mentioned in the comments, this question is different from the one people are saying it is a duplicate of since (for one thing) it includes an expression for the variance and it covers the general case where all coupons have unequal probabilities. The case of calculating the variance for the general case of coupons having unequal probabilities has not been covered anywhere on the site apart from , which this one intends to consolidate along with other approaches to solve this problem.    EDIT: Paper on the solutions on this page submitted to ArXiv: I had a Windows 7 installation on my 1TB SSD laptop with 4 primary partitions. I wanted to install Lubuntu Linux but the process failed with an error which kind of said:     cannot write MBR   It gave me an option to put an MBR somewhere else or to boot without MBR. None of these options worked and it became a useless install. After this failed dual boot attempt, Windows would give a BSOD wit Code 007 ending - translated to inaccessible boot device. That is a huge NTFS partition and I don't think I have any other media to back it up before formatting it.  My only option is somehow rebuilding the old MBR. Hence I started creating a whole bunch of live USB boot environments  including Super GRUB Disk and MiniTool Partition Editor Live CD, but none of this could ever help me recover my lost MBR.  Win PE 4.0 reported the partition as bad disc and the latest version did not even have an option for MBR. I managed to create a live USB with Testdisk Running on Ubuntu. Whatever partition was seen as HPFS on quick  search was written in the MBR and after this the disc is totally unreadable. Earlier I could see my data through Linux and now I can see nothing.  Here are my questions:   When some data could be read (but Windows would not boot) the MBR was shown as dynamic MBR. As far as I know dynamic MBR is a Windows concept and my Linux attempt would not have converted it. While installing Linux I tried to delete 2 primary partitions which I found to be not really useful (I backed up their data first). So I am not sure what created the dynamic MBR.  Did my dual install convert those basic MBR to dynamic MBR? How did that happen? Here is a screenshot of my deep search attempt with TestDisk which is still in progress. I can see 4 NTFS partitions and one of these two system partitions should be the original MBR. When I tried to write both these system partitions (after stopping the deep search momentarily) I got an error like "partition not found". The file system utility showed me that there is no backup sector and that may be the reason why it cannot be read.  What other Resorts do I have, other than doing a plain format and then using some recovery tool to recover all my lost data? I am not even sure I will recover the folder names.  What other options should I be trying to restore my old MBR so Windows can boot?      Update  as of last I managed to create a live USB w/ W7  I used AOMEI Partition assistant 6.0 and on deeper  search I can see the 909 gb partition - it wont let me select it for recovery. I am sorry if my earlier Q was not clear. I referred to restoring an MBR from a partition . What happened earlier  - superficial search revealed all old partitions but NOT this one   and the later partitions showed up on Deep search &amp; I can select Other partitions for recovery but for this one. It wont let me select the partition I want  Here are some more screen shots    So in summary all that happened is   4 primary windows 7 partition -->  wanted to install Linux so I deleted 2 non bootable partitions after backing them up  ended up with BSOD ( inaccessible boot device ) and noticed that some windows partitions showed up as Dynamic MBR  (using Live USB Linux,gparted )  Use standard testdisk procedure to write MBR from the superficial NTFS-HDFS partition.  this is where I screwed up . Hindsight I should have really done a deep search and caught the 901gb partition to write MBR. I am not sure if I can undo this action  after this - life gets worse. I am  on a ventilator ! Now C is unreadable by windows and linux both and testdisk cannot list file ( see screenshots ) and I have been using a series of live USB's with some recovery s/w but no luck. ALL I want is to recreate that 901gb partition and the boot partition and put the MBR on the latter so I can get my windows 7 back again PHP replaces spaces with underscores Prove if f(z) is entire function s.t $|f(z)|\leq M|z|$ then $f(z)$ Is polynomial of degree $1$ Let $f(z)$ be an entire function s.t $|f(z)|\leq M|z|$ ; $M&gt;0$ is a constant then $f(z)$ Is polynomial of degree 1   My try $f(z)$ is entire so it can be written as a $\sum a_n z^n$  $$|\sum a_n z^n|\leq \sum |a_n||z|^n\leq M|z|$$  So $n=1$  Seems that the move $\sum |a_n||z|^n\leq M|z|$ is problematic What's the right course of action for cross-site duplicates?  There are two flavors:   A question is posted which belongs on another site and ends up already having been asked there. I can't find an example right now, but it's bound to happen soon if it hasn't already. The same question is posted in two places at the same time. Take  for example, which is a duplicate of , posted within a half hour of each other by the same user.   Possible actions:   Move it to the proper site and close it once it gets there as a duplicate. Provide a way to close it right away as a cross-site duplicate, without moving it first. Flag it and let a moderator merge them. Close it as "no longer relevant" or something else.   Additionally, flavor 2 is a bit of a special case; perhaps the question really spans both sites in terms of content and intended audience. Should multiple-postings in this case be allowed? If so, should they somehow be linked to each other? If not, how do we avoid a migration war? What are the pros and cons of adding a vapor barrier behind shower backer board? Systems of linear differential equations - eigenvectors When can a (finite) group be written as the quotient of some other group by its center? So if I'm given $H$, when I can conclude there is a group $G$ such that $H\cong G/Z(G)$? It's easy to show that non-trivial cyclic groups are not of this form. More generally, any group with the property that all finitely generated subgroups are cyclic (e.g. $\mathbb{Q},\mathbb{Q}/\mathbb{Z}$) cannot be of this form. Are there are any others? Prove any orthogonal 2-by-2 can be written in one of these forms.... I'd like to prove that any orthogonal $2 \times 2$ matrix can be written   $$\bigg(\begin{matrix}    \cos x &amp; -\sin x  \\     \sin x &amp; \cos x   \end{matrix}\bigg) \hspace{1.0em} \text{or} \hspace{1.0em} \bigg(\begin{matrix}    \cos x &amp; \sin x \\    \sin x &amp; -\cos x \end{matrix}\bigg)$$  for $0 \le x &lt; 2\pi$.  I have no idea how to do this. I feel like this is something I've missed and is really straightforward but I can't find it in my book... I am making a fudge recipe that calls for 1cup whole milk and 5 cups sugar. It also uses 2 sticks of butter and 25 marshmallows. I'm wondering if I can omit the milk and cut back on the sugar by using sweetened condensed milk. Geomagnetic reversal? I have always been told that the geomagnetic field acts "as if" there were a bar magnet inside the Earth. I now this is not true, but I feel that knowing what is actually going on would help me understand the answer to the question that I'm about to ask:  Why does geomagnetic reversal happen? Is it something gradual or relatively fast?  (What is the origin of the geomagnetic field? Can we answer my questions starting from this mechanism? I want to learn more about hopf algebras but I am having trouble finding a down to earth introduction to the subject with lots of motivation and examples. My algebra knowledge ranges from Dummit and Foote, Atiyah-Macdonald commutative algebra, and Hartshorne level algebraic geometry.  What are good places to look at for a hopf algebra beginner? My main motivation is for studying groupoid schemes from an algebraic point of view. Is this a correct way for passing an environment variable in sudo ?  sudo -u www-data -b env FOOBAR="foobar" /home/user/folder/daemon Does an electrolytic capacitor degrade each time it receives reverse voltage? How to make HTML code inactive with comments Disable commandButton after first click to prevent double submission I have an apex:commandButton on a visualforce page that invokes a method on the controller. There is currently no rerender value set for the button. Instead the controller method returns a PageReference to redirect the user as required.  E.g.  Visualforce:  &lt;apex:commandButton value="Save" action="{!save}"/&gt;   Controller:  public PageReference save() {     // save body ...      // return the user the a parent opportunity     return new PageReference('/' + opp.Id); }   Users are currently able to click on the resulting save button multiple times before the controller completes and returns the PageReference to redirect the browser to an opportunity.  How can I disable the commandButton after the first click?    I tried wrapping the commandButton in an actionStatus and facet, but the need to define the rerender property prevented the resulting PageReference redirect.  E.g.  This will render nicely in the browser and prevent multiple clicks, but doesn't redirect to the Opportunity on completion.  &lt;apex:actionStatus id="saveStatus"&gt;     &lt;apex:facet name="stop"&gt;         &lt;apex:commandButton value="Save" action="{!save}" status="saveStatus" rerender="saveParentBlock" /&gt;     &lt;/apex:facet&gt;     &lt;apex:facet name="start"&gt;         &lt;apex:commandButton value="Saving..." disabled="true" status="saveStatus"/&gt;     &lt;/apex:facet&gt; &lt;/apex:actionStatus&gt;     There is a similar question . I need to support an existing PageReference redirect, which slightly alters the requirements.  Force.com Discussion Boards:   Ideas: Creating and configuring .bash_profile I was setting path for anaconda. an answer to a question  has the following solution. I searched for .bash_profile, but I can't seem to find it. How do I setup this file and get it to run on startup?