I have 2 random variables, all independant, discrete and uniform  I want to compute standard deviation for Z = X - Y  Here is the R code:  #create X and Y X = rep(0:1, c(733-41,41)) Y = rep(0:1, c(742-60,60))  #create Z as Y - X Z = c() for (i in X) {Z = c(Z,c(Y-i))}   Means are equal:  mean(Z) [1] 0.02492802 mean(Y) - mean(X) [1] 0.02492802   Then I count standard deviation and variance of Z using the formula:  sd(Y) + sd(X) [1] 0.5027599 var(Y) + var(X) [1] 0.1273021   Ann then, using sd() and var() functions:  sd(Z) [1] 0.3565528 var(Z) [1] 0.1271299   Where is my mistake and why sd(Y) + sd(X) != sd(Z) and var(Z) != var(Y) + var(X)?  Thanks!
Is it (always) true that $$\mathrm{Var}\left(\sum\limits_{i=1}^m{X_i}\right) = \sum\limits_{i=1}^m{\mathrm{Var}(X_i)} \&gt;?$$
I cast  on my opponent, whose hand has two Mountain cards. Wistful Thinking resolves and my opponent draws a  and another Mountain.  Can my opponent cast Shock before discarding it? I tried for a while to classifiy the singularities of $\frac{1}{z}-\frac{1}{\sin z}$ at the origin, but I am stucked. Is there someone who is able to help me at this point? Do I need a transit visa for a layover via airports in the UAE, such as Dubai International Airport or Abu Dhabi International Airport? If so, what are the requirements for such a visa? Can I get the transit visa on arrival? How to identify the process that's sending error messages to terminal? Why does a cordless circular saw have the blade on the left? At the moment considering the purchase of a circular saw for light work. I'm looking at a corded model and a cordless model. But the question I have is not about which one is better.   My question today is why the corded one has the blade on the right of my hand and the cordless one has the blade on the left of my hand. See both models below.     Now, I know some manufacturers make left- and right-handed versions of their circular saw. And I'm also aware that 'worm drive circular saws' usually have the blade to the left of my hand. But it seems odd to me. Especially as it seems to apply to most manufacturers too.   Was wondering if somebody has an explanation for this. I think I have managed to work this out, however there is no solution provided with the question so I thought it best to check.   My working:  Let $(x,y) \in (A \times B) \cup (C \times D)$  $\Rightarrow x \in (A$ or $C)$ and $y \in (B$ or $D)$  $\Rightarrow (x, y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow (A \times B) \cup (C \times D) \subseteq (A \cup C) \times (B \cup D)$  Now let $(x,y) \in (A \cup C) \times (B \cup D)$  $\Rightarrow x \in (A$ or $C) $ and $y \in (B$ or $D)$  $\Rightarrow (x, y ) \in (A \times B) \cup (A \times D) \cup (C \times B) \cup (C \times D)$  $\Rightarrow (A \cup C) \times (B \cup D) \nsubseteq (A \times B) \cup (C \times D)$  $\Rightarrow (A \times B) \cup (C \times D) \not= (A \cup C) \times (B \cup D)$  Is this correct?  Thank you. Formatting each part/section/subsection Are there some magic lines to be placed in the preamble that would, like in CSS,  specify how each generic section or subsection in the whole document should be formatted? I am simply adding user in 'Monitored Users' in Debug Logs. But User is not getting added. How can I disable Ctrl+Q for all applications (system wide)? A lot of applications like Firefox, Chrome etc, get closed when I accidentally press Ctrl+Q instead of Ctrl+W because of the proximity of the Q and W keys on the keyboard. Is there a way this shortcut can be removed or reset on a system wide basis? Why are integer literals with leading zeroes interpreted strangely? How do I use 'chmod' on an NTFS (or FAT32) partition? How to display Trash and Home folder icons? Mod shows up with OP background when viewing deleted comments Can I travel to France with Fiktionsbescheinigung (Fiction Certificate) of Germany Are the PUT, DELETE, HEAD, etc methods available in most web browsers? I've seen a couple questions around here like , which mentions:     Unfortunately that same browser won't allow me to test HTTP PUT, DELETE, and to a certain degree even HTTP POST.   I've also heard that browsers support only GET and POST, from some other sources like:        However, a few quick tests in Firefox show that sending PUT and DELETE requests works as expected -- the XMLHttpRequest completes successfully, and the request shows up in the server logs with the right method. Is there some aspect to this I'm missing, such as cross-browser compatibility or non-obvious limitations? "It really doesn't matter" v "It doesn't really matter" On which Stack Exchange site should I post subjective questions? Want to copy the file name quickly in Windows. I always use rename, copy , but feel it is quite slow. Any better way? How are strings passed in .NET? What is Stack Overflow's business model? I once , but that was . Now, , and they have , but where's the business model? The  its own Q&amp;A about its site (since it wasn't included in the ), and just about the only dig in there that halfway has merit is the business model dig:  We switched to a premium model to keep out of the Venture Capital business (been there, done that, got the t-shirt). Companies like StackExchange couldn't do it without the VC cookie jar. Where's the model? Huh, Spolsky? (I’m sorry. Did that slip out?)  It hurt, but I can't help but wonder if they're on to something.  How would Stack Overflow Internet Services pay back the VCs? Ad revenue alone?  There is only one 'paid' product, Stack Overflow careers, but it doesn't seem like that could sustain a business as large as Stack Overflow (Joel once mentioned on his blog that his jobs board brought in an extra million a year in revenue). So what does Stack Overflow do when the VC cash runs out? Is this a get-big-and-take-the-company-public maneuver? Is that the only viable business model for Stack Exchange? Edit: With the size of Stack Overflow's team, it isn't a stretch to say that payroll is at least $2 million  a year, probably as much as 4 when you think about benefits (average 120K for a developer in New York City; x2 for benefits/taxes/all-that-other-good-stuff). Office space can't be cheap, so how long does $6 million last before you need another VC infusion?