I'm fitting some data with a pdf that is the mixture of two gaussians with the same mean (this is, the sum of the density functions). The weight of each gaussian after the fit is $w_{\rm core}$ and $w_{\rm tail}$, $$ f_{\rm Global} ( \mu, \sigma_{\rm core}, \sigma_{\rm tail} ) = w_{\rm core} N(\mu, \sigma_{\rm core}) + w_{\rm tail} N(\mu, \sigma_{\rm tail}) $$ , where $N(\mu, \sigma)$ is the normalized normal distribution Is there an analytical expression to compute the variance of the global pdf (as a function of $w_{\rm core}$, $w_{\rm tail}$, $\sigma_{\rm core}$ and $\sigma_{\rm tail}$)?  Answer $$ \sigma_{\rm Global}^2 = w_{\rm core} \sigma_{\rm core}^2 + w_{\rm tail} \sigma_{\rm tail}^2 $$ This is derived in  for the general case $\mu_{\rm core} \neq \mu_{\rm tail}$. I'm quoting it in case somebody searches directly for the specific case (like me) and does not find the other answer.
Say I have two normal distributions A and B with means $\mu_A$ and $\mu_B$ and variances $\sigma_A$ and $\sigma_B$. I want to take a weighted mixture of these two distributions using weights $p$ and $q$ where $0\le p \le 1$ and $q = 1-p$. I know that the mean of this mixture would be $\mu_{AB} = (p\times\mu_A) + (q\times\mu_B)$.  What would the variance be?    A concrete example would be if I knew the parameters for the distribution of male and female height. If I had a room of people that was 60% male, I could produce the expected mean height for the whole room, but what about the variance?
I don't know much more about SEO, but it's interesting to learn about it. When I tried to search my website with an associated keyword or you can say with the exact name of the domain, I got some suggestions by Google. Here's .  First of all, I don't want to spamming here, I just want prove my question and want to give a hint about what I am talking here. The above link display the Did You Mean, I know the specific reason why Google shows this, but I want to know the Google's guidelines and some guidance by you experts so that if someone search for the particular keyword then Google hide that Did You Mean and display the result. Where can I find a list of computers guaranteed to work with Ubuntu? Before I buy my next laptop, I'd like to make sure that it will work perfectly with Ubuntu. Is there a list of completely supported computers anywhere? "contribute to investigating" or "contribute to investigate" I'm trying to find, which of the following sentences is correct?  A) We try to highlight how they contribute to investigate their importance. B) We try to highlight how they contribute to investigating their importance.  I found that both cases were used frequently in formal writing. Edited: Sources for each case: For A: &quot;Their multifaceted nature means that there are very many routes to investigating their importance for understanding social change&quot; in &quot;A lineage for contemporary inter-city studies&quot; book. B: &quot;More factors are analysed to investigate their importance in scoring from shots and shot probabilities&quot; in &quot;Applications of logistic regression to shots at goal at association football&quot; book. If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p. If p $\equiv$ 3 (mod 4) with p prime, prove -1 is a non-quadratic residue modulo p.  I suppose this would not be true if p $\equiv$ 1 (modulo 4).  To prove something is a non-square I find to be tricky. It's difficult to see any straightforward way to do this using only the definition of congruence for example. Does using the Console Commands negatively affect me? I'm wondering in case I get stuck in an area that I'm unable to get out of or if I clip into a wall and I suddenly can't move. I've had to disable clipping to get out of certain areas in Skyrim before but I want to make sure that things like my achievements and stuff won't shut out on my playthrough.  If I enable something, spawn an item that didn't spawn for me, or just basically use the console command to fix any bugs, what will happen achievement and game-wise? I'm taking a course on waves and oscillations using Crawford from the Berkeley series (out of print excluding international copies), and would like to know if anyone has any suggestions for a better book. We cover:    coupled oscillators, forced oscillators,  Fourier analysis,  traveling waves,    and some other topics. Any help with the topic would be appreciated. I have a bit of code where I've written a SOQL query that returns a list of SObject records, however I need a Set&lt;Id&gt; structure to pass to another method that I don't have control of (and thus can't change the method signature of).  How can I turn my returned List&lt;SObject&gt; into a Set&lt;Id&gt;? Is the best option just a for loop? Seatpost Overextension I've been riding with my very short seat post extended well past its maximum extension line for quite a while now. Looking at the seat post itself I don't see any signs of deformation or damage other than some very minor surface rust.   Could my bike frame have been damaged? Could the lever force have damaged the frame? I can post some pictures of the frame if needed. My bike is all aluminum. How can I stop being prompted to unlock the 'default' keyring on boot? Whenever Ubuntu boots up, a dialogue pops up asking me to unlock my default keyring. Is there some way this can unlock automatically through PAM or some other magical way? I just got this error message for the first time (I was getting this as the response to any request on the SE network for about the last five minutes, until now):     We're sorry...      There are an unusual number of requests coming from this IP address.   To protect our users, we can't process any more requests from this IP   address right now. We'll restore access as quickly as possible, so try   again soon. If you believe you have reached this page in error,   contact us.   As far as I know, I was not spamming SE or participating in DOS attack, and I find it unlikely that any of my office coworkers who share my IP address were doing so either.  Granted, I was pressing F5 a lot. But I've always pressed F5 a lot on SE, and have never gotten this message before. So my question is: Is it possible to get this error message simply by refreshing too much or too often? Or is that message reserved for a truly massive number of requests that are unlikely to be caused by one person refreshing a lot? (In the former case, I can't explain why I've never gotten it before; in the latter case, I can't explain why I just got it now). When to use "cannot" versus "can't"? When is it best to write "can't" versus writing "cannot"? Are they interchangeable in every situation? Integrate JavaScript in JSF composite component, the clean way In CodeGear Delphi 2007, how can I turn specific warnings and hints off? I am attempting to turn off H2077 - Value assigned to 'varname' never used. Dropping one of the columns when using one-hot encoding My understanding is that in machine learning it can be a problem if your dataset has highly correlated features, as they effectively encode the same information.  Recently someone pointed out that when you do one-hot encoding on a categorical variable you end up with correlated features, so you should drop one of them as a "reference".  For example, encoding gender as two variables, is_male and is_female, produces two features which are perfectly negatively correlated, so they suggested just using one of them, effectively setting the baseline to say male, and then seeing if the is_female column is important in the predictive algorithm.  That made sense to me but I haven't found anything online to suggest this may be the case, so is this wrong or am I missing something?  Possible (unanswered) duplicate: List comprehension with expensive computation How can I use an array of function pointers? How should I use array of function pointers in C?  How can I initialize them? Is there really no English equivalent to German's “Fachidiot”? There was the following paragraph in the article that came under the title, “GOP and the rise of Anti-knowledge” written by  (October 29, 2015):     “English unfortunately doesn’t have a precise word for the German   “Fachidiot,” a narrowly specialized person accomplished in his own   field but a blithering idiot outside it. In any case, a surgeon is   basically a skilled auto mechanic who is not bothered by the sight of   blood and palpitating organs. We need the surgeon’s skills on pain of   agonizing death, and reward him commensurately but that does not make   him a Voltaire.”    In Japanese we have a word, 専門バカ, of which literal translation is “specialist idiot” meaning exactly same as defined the above - a narrowly specialized person accomplished in his own field but a blithering idiot outside it.  I’m really curious about the absence of short descriptions of the specialist who knows nothing more than his specialty area in English like German “Fachidiot,” and Japanese "専門バカ."  Isn’t there really any short word counterpart to “Fachidiot,” specialist’s ignorance, for instance, in English?  P.S.  I found "narrow-minded specialisit" as a German-to-English translation of "fachidiot" in the web site, Interglot translation dictionary. How to change launcher icon Is there a way to customize a Lucid Lynx Launcher icon for various programs? There does not seem to be a way to do this using Create Launcher or Launcher properties. The application is not actually "installed" on the PC, the executable has just been copied. All I've been able to do so far is to add the command /home/t32/bin/pc_linux/t32marm -c /home/t32/config_usb.t32 to a generic Launcher icon using Create Launcher. How do I access folders created on Ubuntu with Windows? Deputy badge after a reputation of 3000