The distribution of the product of Gaussian variable and Rademacher variable.
Distribution of Product of Random Variables with one being the normal distribution.
How to change the starting reference number in Natbib in a given bibunit? I'm using bibunit and Natbib packages with a numerical numbering.   \begin{bibunit}[plainnat]     \nocite{ref1,ref2}     \putbib[mybiblio] \end{bibunit}  \begin{bibunit}[plainnat]     \nocite{ref3,ref4}     \putbib[mybiblio]  \end{bibunit}   How can I set the starting number for ref3 and ref4 to be different from 1 (say 15), without affecting the starting number for ref1 and ref 2? The desired result is the following:   [1] ref 1 [2] ref 2 [15] ref3 [16] ref4 why is there no non-degenerate 2-forms on 4-sphere? I'm getting "jumpy" loadings in rollapply PCA in R. Can I fix it? Under what condition we can interchange order of a limit and a summation? Probability that the sum of 6 dice rolls is even 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 No feedback when comment fails to post on Android 2.3.5 In the mobile theme on Android 2.3.5, comments that do not meet the minimum length will fail to post but no feedback message is displayed to the user.  The submit button changes to its active state, but nothing else happens. What is meant by "obfuscate by pretending"? I came accross the following sentence:  "Politicians obfuscate by pretending that the world would be the same if it weren't for the Cold War."  What is the meaning of obfuscate by pretending and how does it relate to the rest of the sentence?  The way I understood it: politicans are aware that the world would not be the same if it weren't for the Cold War, but are (due to unknown or suspected reasons) not willing to admit this and therefore pretend otherwise. Unknown apps/processes with number only are shown in the battery screen I have a dataset in csv file format that I'm loading into pgfplotstable. I can't change the format of the original csv, and being financial data it has a column of item names and two or three explanatory data points at the top of the table. e.g.  \documentclass{article} \usepackage{array,datatool,pgfplotstable}   \begin{filecontents}{sample.csv}     item,2008,2009,2010,2011      ,Actual,Actual,Forecast,Forecast      ,GBP,GBP,GBP,GBP      ,('000),('000),('000),('000) rounded     Area 1 OP, 1000000,1500000,1750000,250000     Area 2 OP, 400000,500000, 450000,-50000     Area 51 OP, 300000,375000,390000,15000     No P, 1250000, 1000000, 950000, 50000     Residuals, 800000, 80000, 90000, 10000   \end{filecontents}  \pgfplotstableread[col sep=comma]{sample.csv}\mystuff   I'm stumped at the next stage which is to typeset \mystuff so I have comma separators and can add a row that sums the 'Area' columns. At the moment to display the table I have to do something like  \begin{document}  \pgfplotstableread[col sep=comma,header=false]{sample.csv}\mystuff  \pgfplotstabletypeset[   columns/0/.style={string type},   columns/1/.style={string type},   columns/2/.style={string type},   columns/3/.style={string type},   columns/4/.style={string type}]\mystuff  \end{document}   How do I tag the top three rows as string and the rest of the last four columns as integer type so I can format and transform them? remote action function encountering CPU time out limit exception Why isn't temperature frame dependent? In (non-relativistic) classical physics, if the temperature of an object is proportional to the average kinetic energy ${1 \over 2} m\overline {v^{2}}$of its particles (or molecules), then shouldn't that temperature depend on the frame of reference - since $\overline {v^{2}}$ will be different in different frames?  (I.e. In the lab frame  $K_l = {1 \over 2} m\overline {v^{2}} $, but in a frame moving with velocity $u$ relative to the lab frame, $K_u =  {1 \over 2} m \overline {(v+u)^{2}}$). Seems like a stupid question, but I'm after a nice solid answer if possible.  I joined SO a while ago to ask the odd question, but recently I'm starting to use it more often.  I've been reviewing the 40 max items (20 first posts/20 late answers) per day, and editing anything I see wrong with them (lots of +2's)... flagging them... etc.  I've also been  per day.  But other than commenting where I can and answering the odd question, I'm only  (1k at the moment).  I might just be overeager, but I was hoping some high-rep users might be able to write a little something on how they earned their stripes?  I've , and to be honest I was hoping I'd get a hit, because it sounds like a stupid question... anyways, here you go!  Also, I'm not referring to how to gain rep on Meta, since it's a bit of a fluke I've earned the rep I have on here. I'm asking about main SO. How do I count the number of occurrences of a char in a String? Is There a Difference Between Taxonomies and Categories? I've been reading the codex for WordPress closely and am confused about the vague definitions between what a Taxonomy is and what a Category is. For that matter, term is also a word that is used in the description of Taxonomies, but seems used in a manner that hints that it isn't solely limited to a Taxonomy.   Both are described as a way to classify and group together posts. I do understand that Taxonomies are a more general form of categories, but how exactly do they relate to each other?   Is there a subtle difference I'm just not picking up on? Is Meta Stack Overflow just the meta for Stack Overflow or is it a somewhat special meta site? Initially I thought that Meta Stack Overflow was the common meta for all SE sites.   Then I noted that  has its own meta site.   It took a while for me to learn that even Server Fault has its own meta site.  Looking at my reputation points, I see difference between Stack Overflow and Meta Stack Overflow, but not between the other sites and there corresponding meta sites.  Now, is Meta Stack Overflow in some sense the master meta site of all or not? Proof by induction of summation inequality: $1+\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+\dots+\frac1{2^n}\ge 1+\frac{n}2$ Im having trouble with the second part of this question,  Let $H$ be a normal subgroup of $G$ with $|G:H| = n$,  i) Prove $g^n \in H$ $\forall g \in G$ (which i have done)  ii) Give an example to show that this all false when $H$ is not normal in $G$.(which I am having trouble with showing)  Any suggestions? Declare variable to hold job name and if job running kill it I’m looking for a single file that does these things in order.   Declare a variable to hold a job name  Run a query to check whether that job declared is currently running Set up an if loop If the job is running, execute the stored procedure that kills it.   My question is to write a query that declare a variable to hold a job name and gives us result the job is still running or not if the job is running execute the stored proc to kill it.  My manager was asking me to listing running jobs and suspended jobs and declare a variable to hold job name and setup an IF loop like if job is running run proc to kill it. Quadratic models with R. The use of poly(..) and I(..) functions (R-language) What causes the different results below?    var1 = c(0.04875,0.13725,0.28350,0.50975,0.77425,0.94700,0.05325,0.14050,0.29725,0.51525,0.79000,0.95400,0.04625,0.15250,0.29000,0.53300,0.79825,0.95225,0.05025,0.14625,0.28800,0.52625,0.78200,0.95925,0.04700,0.14225,0.30325,0.53500,0.79325,0.95875,0.04775,0.13850,0.28675,0.54250,0.78300,0.95175,0.05150,0.12725,0.30175,0.54725,0.79475,0.96275,0.05375,0.14100,0.30050,0.53275,0.78100,0.96175,0.05450,0.15300,0.29650,0.52850,0.80100,0.95675,0.05425,0.13975,0.30875,0.56025,0.80575,0.96100,0.05100,0.15350,0.31175,0.53300,0.78900,0.96000,0.04650,0.13525,0.29600,0.53625,0.78475,0.96375,0.05375,0.13900,0.29600,0.53725,0.78700,0.95800,0.05075,0.14350,0.29225,0.54525,0.80275,0.95800,0.05050,0.13200,0.29850,0.52700,0.80525,0.96150,0.05150,0.14050,0.29450,0.54375,0.79450,0.96375,0.05375,0.13525,0.30475,0.55250,0.79425,0.96025,0.04950,0.14500,0.29425,0.52250,0.78475,0.95650,0.05225,0.14425,0.29225,0.53150,0.80425,0.95375)  var2 = c(1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6)  var3 = c(4,4,4,4,4,4,6,6,6,6,6,6,8,8,8,8,8,8,10,10,10,10,10,10,12,12,12,12,12,12,14,14,14,14,14,14,16,16,16,16,16,16,18,18,18,18,18,18,20,20,20,20,20,20,22,22,22,22,22,22,24,24,24,24,24,24,26,26,26,26,26,26,28,28,28,28,28,28,30,30,30,30,30,30,32,32,32,32,32,32,34,34,34,34,34,34,36,36,36,36,36,36,38,38,38,38,38,38,40,40,40,40,40,40)   summary(aov(var1~as.factor(var2)*var3)) summary(aov(var1~as.factor(poly(var2,1))*poly(var3,1)))   I might not understand well how poly(..) and I(..) work. Could you give me some hints about these two functions?  (I aim to create models of different degree (quadratic, cubic, etc..) and compare their BIC (or AIC)).