When setting up a server, I was told it needs to have really good fault tolerance. What RAID array would give me the best fault tolerance?
This is a  about RAID levels.    What are:   the RAID levels typically used (including the RAID-Z family)?  deployments are they commonly found in? benefits and pitfalls of each?
The limit of a convergent Gaussian random variable sequence is still a Gaussian random variable I'm trying to prove this conclusion but have some problems with one of the steps.  Assume $X_1,\ldots,X_n,\ldots$ is a sequence of Gaussian random variables, converging almost surely to $X$, prove that $X$ is Gaussian.  We use characteristics function here. Since $|\phi_{X_n}(t)|\leq 1$, by dominated convergent theorem, we have for any $t$  $$ \lim_{n\rightarrow\infty}e^{it\mu_n-t^2\sigma_n^2/2}=\lim_{n\rightarrow \infty}\phi_{X_n}(t) = \lim_{n\rightarrow \infty}\mathbb{E}\left[e^{itX_n}\right] = \mathbb{E}\left[e^{itX}\right] = \phi_X(t) $$  this is the step that I cannot figure out: $e^{it\mu_n-t^2\sigma_n^2/2}$ converges for any $t$ if and only if $\mu_n$ and $\sigma_n$ converges.   Let $\mu=\lim_n \mu_n$, and $\sigma=\lim_n\sigma_n$, then $\phi_X(t)=e^{it\mu-t^2\sigma^2/2}$, which proves that $X$ is a Gaussian random variable.  Why can we get that $\mu_n$ and $\sigma_n$ converge? This looks intuitive for me, but I cannot make a rigorous prove. Adding more than 15 digits in Excel I want to add more than 20 digits in an Excel cell.  The current format of the cell is general, it converts the number to an exponential format. I tried with a number format and accounting, but when I enter more than 15 digits it gets converted to 0's.  What are the recommended steps for stopping Excel from converting data to exponential Format for 20 digits when in the general format?     Example: 12345678901234567890   Excel converts it to 1.23457E+19 in general format.  Without using ' before the value, is there any other way to keep value same? Is there a way to send a thanks message to Stack Overflow or any of the individual Stack Exchange sites, aside from sending an email? I want to thank Stack Overflow for being an awesome live QA site. It helps people a lot. What is the width of the standard paragraph indent in LaTeX's article class? If no changes has been made to the settings of indentation of an article class LaTeX document, what is the width of the paragraph indent?  texdoc article in the terminal opens the Standard Document Classes for LaTeX version 2e manual. In section 6.2 Paragraphing I find the following line:  ⟨10pt⟩ \setlength\parindent{15\p@}   The  means 1pt ... so I guess this would mean that the standard indent is 15 pt at a 10 pt text size? Is this correct? I am using latest version of VirtualBox (VirtualBox 4.3.6 for Windows hosts) and after installing any OS and clicking inside of it mouse disappear. It is not visible until I press right CRTL. Anyone know what can cause this problem. I have also installed extension pack. How well does T-Mobile's (US) Simple Choice plan work when in Europe? What, precisely, is a confidence interval? I know roughly and informally what a confidence interval is.  However, I can't seem to wrap my head around one rather important detail:  According to Wikipedia:     A confidence interval does not predict that the true value of the parameter has a particular probability of being in the confidence interval given the data actually obtained.     I've also seen similar points made in several places on this site.  A more correct definition, also from Wikipedia, is:     if confidence intervals are constructed across many separate data analyses of repeated (and possibly different) experiments, the proportion of such intervals that contain the true value of the parameter will approximately match the confidence level   Again, I've seen similar points made in several places on this site.  I don't get it.  If, under repeated experiments, the fraction of computed confidence intervals that contain the true parameter $\theta$ is $(1 - \alpha)$, then how can the probability that $\theta$ is in the confidence interval computed for the actual experiment be anything other than $(1 - \alpha)$?  I'm looking for the following in an answer:   Clarification of the distinction between the incorrect and correct definitions above. A formal, precise definition of a confidence interval that clearly shows why the first definition is wrong. A concrete example of a case where the first definition is spectacularly wrong, even if the underlying model is correct. Acces VBA code combination not working, issue with exit sub? I'm very new at VBA and I can't seem to solve this problem. It seems like it should be an easy problem to fix, I just don't know how.   So what the code does: In the main form is a record. This record will be copied to another table bij pressing a button on the form. Before the copying begins, the code checks first if the 'OMnummer' has been filled in in the subform.  If not, a message box appears saying that the user should fill in the subform and the code stops running.   Secondly the code checks if the record is allready present in the other table. If so, a messagebox appears and the record will not be copied. If not, the record will be copied to the other table.   Both pieces of code work ok seperately. However, when I try to include both pieces in the same private sub, only the first one works. It may be something with the 'Exit Sub' code or I am not using the If - Then right.   Hope you can help me!  Monika   Private Sub KnopProjectVersturen_Click() On Error GoTo ErrProc  If IsNull(Me!Subform_OMnummers.Form!Omnr) Then  If MsgBox("Vul het OMnummer in. Je kan het project niet exporteren zonder OMnummer.")     Then       Exit Sub      DoCmd.OpenQuery "Qry_Depo_ControleAanwezig"  If DCount("Deponering.projectnummer", "Qry_Depo_ControleAanwezig") = 0 Then         DoCmd.SetWarnings False         DoCmd.OpenQuery "Qry_projectnaarDepot"          DoCmd.OpenQuery "Qry_ToevoegProjectDepot"         DoCmd.OpenForm "Depot_uitvoer", , , "[Projectnummer] = '" &amp; Me![Projectnummer] &amp; "' And [subID]=[subID]"     Me.Status = 8     DoCmd.Close acQuery, ("Qry_Depo_ControleAanwezig")     DoCmd.SetWarnings True  Else         MsgBox "Dit project bestaat al in de Depot_Uitvoer, verander de status in het projectformulier", vbInformation, "Example"         DoCmd.Close acQuery, ("Qry_Depo_ControleAanwezig")     End If  End If  End If    'Als er fouten zijn laat deze code een messagebox zien met het nummer en de melding.  ExitProc:  Exit Sub  ErrProc:     Select Case Err.Number     Case Else         MsgBox Err.Number &amp; "--" &amp; Err.Description         Resume ExitProc         End Select End Sub How do natural and weapon attacks mix? I have a level 1 Synthesist Summoner.  Since he has the Quadruped base Eidolon, when fused, my Summoner has a bite attack (Primary). In addition, I have spent evolution points on a tentacle (Secondary). Finally, my Synthesist carries around an Axe, with which he can make weapon attacks.  If I were to use the Full-Attack option, what attacks could I make, and at what penalties? Let's assume I want to always use the Axe, where possible.  How does this interact with the eidolon's natural attack limit? (3 at first level) I was just wondering about that because it would influence how I deal with closed questions, e.g. whether they need to be improved (tagging, formatting, code samples) after closing, or if some should be deleted altogether.  However, I'm not asking for answers to these questions, I just want to know if Google (and/or other search engines) list closed questions in their search results. (I hope they don't.) Is 'hair' singular or plural? When one says I was washing my hair, is it singular or plural? What is the singular for hair? Wild Magic Surge - What does "You cast ..." mean for your spell slots? In response to  question, I started to think about what it means when a Wild Magic Surge results in a "You cast spell-X".  So, "specific beats general" gives:   You can cast a second spell when you would not normally be allowed to You can cast a spell you don't know If the surge forces you to cast a concentration spell you would lose any concentration spell that you currently had active Subject to what the specific entry says you can target it how you like Unless the specific entry prohibits it you could use metamagic on the spell   I am pretty confident in all of the above but if anyone disagrees please address in an answer.  Here comes the question.  How does this impact on your available spell slots?  "You cast ..." to me suggests that if you have an applicable slot available then you have to use it to cast the spell because that is the general rule for casting spells but if you don't then "specific beats general" and it is cast anyway.  Specific examples:     You cast fireball as a 3rd-level spell centered on   yourself   This must be a 3rd level spell:   if you have a 3rd level slot available you have to use it? if you don't, if you have 5 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?      You cast confusion centered on yourself.   No level specified and confusion is a 4th level spell:   if you have a 4th level slot available you have to use it? if you have a 4th, a 6th and an 8th level slot you can choose which one to use? if you have only a 5th level slot but also 6 sorcery points and a bonus action, you could choose to use the 5th level slot or use the points to create a 4th level slot? if you don't have any 4th level or higher slots but you have 6 sorcery points and a bonus action available must you use these to get that slot? if you don't have any of that then the spell goes off anyway?   And so on ... Sakurai QM section 5.8 If anyone is familiar with Sakurai's book, specifically section 5.8 on energy shift and decay width, I am stuck and could use some help. I can't see how he derives 5.8.9 (in the revised edition). He starts with (3) (given below), and derives (1) and (2). The equation is as follows:$$(1){\space}{\space}\space{\space}\space{\space}{\dot c_i\over c_i}\approx{{-i\over \hbar}V_{ii}+{\left(-i \over \hbar\right)}^2{{{\left|V_{ii}\right|}^2}\over \eta}+\left({-i\over \hbar}\right) {\sum_{m\not=i}}{{{\left|V_{mi}\right|}^2}\over {(E_i-E_m+i\hbar\eta)}} \over 1-{i \over \hbar}{V_{ii} \over \eta}} $$ $$(2)\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\approx{-i\over \hbar}V_{ii}+\left({-i\over \hbar}\right) {\sum_{m\not=i}}{{{\left|V_{mi}\right|}^2}\over {(E_i-E_m+i\hbar\eta)}}$$ where $$(3)\,\,\,\,\,\,\,\,\,c_i(t)=\lim_{\eta\to 0}\left({1-{i\over \hbar\eta}V_{ii}}{e^{{\eta}t}}+{{\left({-i\over \hbar}\right)}^2}{{\left|V_{ii}\right|}^2}{e^{2{\eta}t}\over 2{\eta}^2}+\left({-i\over \hbar}\right){\sum_{m\not=i}{{{{\left|V_{mi}\right|}^2}}\over 2\eta(E_i-E_m+i{\hbar}\eta}}\right)$$First of all, he discards all kinds of terms in the denominator of the first expression, and I can't see how he justifies this, because as ${\eta}\to0$, every term in the expression for $c_i(t)$ blows up (besides the 1 of course). Then he seems to multiply top and bottom by the complex conjugate of the denominator in (1), arriving at (2). He seems to discard a term from the denominator here, which is of second order in V, and says the equation is formally correct up to second order. This doesn't make sense to me! Also, soon after, he has this strange expression with $$\lim_{x\to 0} {1\over(x+iε)}=Pr.(1/x)-iπδ(x)$$ What is this Pr symbol? Any help would be much appreciated! I don't understand, because if 'don't' is 'do not' then wouldn't the sentence without conjunctions be 'do not you dare' which I'm pretty sure isn't grammatically correct. Like, when we say the term it means something else, certainly not 'do not you dare' anyway. Any ideas on why? I am so glad English is my first language. Requesting raw data from previously published research What do we mean by hyperparameters? I would like to have an app include a custom font for rendering text, load it, and then use it with standard UIKit elements like UILabel. Is this possible? How to enable sleep/standby on Windows Server 2012 Hyper V How does electricity propagate in a conductor? Probability of lim sup, lim inf for sequence of random variables. Maybe this is extremely simple, but i havent found a specific answer for this online.  For a sequence of independent continuous random variables $X_n$ ,$n=1,2,3,...$ , all with the same probability density function $f(x)&gt;0$ for all real $x$, and a specific real number $b$, what do the following events mean in simple terms and what is the probability of each?  a)$\lim_n\sup\{X_n \gt b\}$ b)$\lim_n\inf\{X_n \gt b\}$ c)$\lim_n\sup\{X_n \le b\}$ d)$\lim_n\inf\{X_n \le b\}$