β′xi+ (ρσ)(ϕ(α′zi))/(Φ(α′zi)) ............How this has come, especially the numerator part (ρσ)(ϕ(α′zi)? Could you explain in a simple and lucid way? Also, if you could provide proof step by step with proper explanation.
Say I have two independent random variables $X \sim N(u_1, \sigma_1)$ and $Y \sim N(u_2, \sigma_2)$. I want to get the conditional distribution of X given whether X is bigger than Y or not.  $P(X|X&lt;Y)$ = ... and  $P(X|X&gt;Y)$ = ...  I am thinking solving this in this way:  \begin{align} P(X|X&lt;Y) &amp;= \frac{P(Y&gt;X|X)P(X)}{P(Y&gt;X)} \\ &amp;= \frac{(1-\Phi(\frac{x-\mu_2}{\sigma_2}))N(\mu_1,\sigma_1)}{\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})}\\ P(X|X&gt;Y) &amp;= \frac{P(Y&lt;X|X)P(X)}{P(Y&lt;X)} \\ &amp;= \frac{\Phi(\frac{x-\mu_2}{\sigma_2})N(\mu_1,\sigma_1)}{1-\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})} \end{align}  My questions are:   (1) Whether above solution is correct  (2) How to get the mean and sd for $P(X|X&lt;Y)$ and $P(X|X&gt;Y)$ if they are still normal?
When should I use the subjunctive mood? In which cases should I use the subjunctive mood?     I suggest that every applicant fill out the form carefully.        If she were rich, she would live on Long Island. Why do I get more satisfaction out of participating in SO than out of my job? Alternatively, are there good ways to get more satisfaction out of my job, possibly by leveraging my participation in SO? Arriving at a different port of entry in the same state in USA? Control 220V AC line using MCU In the book &quot;Quantum Mechanics and Path Integrals&quot; Feynman &amp; Hibbs state that  the probability $P(b,a)$ to go from point $x_a$ at time $t_a$ to the point $x_b$ at the time $t_b$ is $P(b,a) = \|K(b,a)\|^2$ of an amplitude $K(b,a)$ to go from $a$ to $b$. This amplitude is the sum of contributions $\phi[x(t)]$ from each path. $$ K(b,a) = \sum_{\text{paths from $a$ to $b$}} \phi[x(t)]$$ The contributions of a path has a phase proportional to the action $S$: $$ \phi[x(t)] = \text{const}\ e^{(i/\hbar)S[x(t)]}$$  Why must the contribution of a path be $\sim e^{(i/\hbar)S[x(t)]}$? Can this be somehow derived or explained? Why can't the contribution of a path be something else e.g. $\sim \frac{S}{\hbar}$, $\sim \cos(S/\hbar)$, $\log(S/\hbar)$ or $e^{- (S[x(t)]/\hbar)^2}$ ? Edit: I have to admit that in the first version of this question, I didn't exclude the possibility to derive the contribution of a path directly from Schrödinger's equation. So answers along this line are valid although not so interesting. I think when Feynman developed his formalism his goal was to find a way to quantize systems, which cannot be treated by Schrödinger's equation, because they cannot be described in terms of a Hamiltonian (e.g. the Wheeler-Feynman absorber theory). So I think a good answer would explain Feynman's Ansatz without referring to Schrödinger's equation, because I think Schrödinger's equation can only handle a specific subset of all the systems that can be treated by Feynman's more general principle. Custom Layout in android How to include custom non-system folder under This PC in Windows 8.1? I've recently upgraded from Windows 8 to 8.1 and noticed the restructured This PC folder, formerly Computer.   What I want to achieve is to include custom folder under "This PC".    What I've found after googling is that what is displayed under "This PC" is stored in registries under   HKEY_LOCAL_MACHINE\SOFTWARE\Microsoft\Windows\CurrentVersion\Explorer\MyComputer\NameSpace  However those folders (such as Desktop, Documents, etc) are referenced via CLSID and the folder I want to include in the list does not have CLSID. You require a reputation of 50 to leave comments on others' questions/answers; the FAQ simply states this as a fact but does not explain it. I'm a new user and I have identified this as an issue very quickly through my own experiences so far. Looking at other questions seems to also provide justification against this 50 reputation requirement for comments on others' questions/answers.      In my own experience, I've seen a few questions like "how do I do x?" then the same poster has answered with "in the end I did it like this: ..." where their solution was perfectly sensible, but there may be some gotchas to watch for - in this case I want to vote up their answer and/or comment on it to point out the potential gotchas, but I can do neither!  To me all of the above seems justification against this rep requirement to comment, so what is the counter-argument and justification for it? $ a\in \Bbb Z_n$ is invertible $\,\Rightarrow\gcd (a,n) =1$ Stealing and reattaching a running process It's sunday and I left an instance of R running in the office. The script finished running, and I would like to save my workspace without going to the office. I can ssh to the computer, but I have not run the program into screen.  Is there a way, over ssh, to disown the process (I don't have access to jobsid of the terminal the program is running on!) and reattach it with say, reptyr? Reptyr and reptyr -T don't work without previously disowning the process  28845 3diag       20   0  139.3m  10.4m   0.0  0.1   0:12.06 S  `- urxvtd                                                                                        5327 3diag       20   0   16.4m   4.6m   0.0  0.1   0:00.02 S      `- bash                                                                                      5335 3diag       20   0 3499.3m 3.244g   0.0 43.3 171:57.89 S          `- R    The unique part of my question is that I explicitly require to detach a program without having access to the terminal in which it was created. Background I'm working on a time series data set of energy meter readings. The length of the series varies by meter - for some I have several years, others only a few months, etc. Many display significant seasonality, and often multiple layers - within the day, week, or year. One of the things I've been working on is clustering of these time series. My work is academic for the moment, and while I'm doing other analysis of the data as well, I have a specific goal to carry out some clustering. I did some initial work where I calculated various features (percentage used on weekends vs. weekday, percentage used in different time blocks, etc.). I then moved on to looking at using Dynamic Time Warping (DTW) to obtain the distance between different series, and clustering based on the difference values, and I've found several papers related to this. Question Will the seasonality in a specific series changing cause my clustering to be incorrect? And if so, how do I deal with it? My concern is that the distances obtained by DTW could be misleading in the cases where the pattern in a time series has changed. This could lead to incorrect clustering. In case the above is unclear, consider these examples: Example 1 A meter has low readings from midnight until 8AM, the readings then increase sharply for the next hour and stay high from 9AM until 5PM, then decrease sharply over the next hour and then stay low from 6PM until midnight. The meter continues this pattern consistently every day for several months, but then changes to a pattern where readings simply stay at a consistent level throughout the day. Example 2 A meter shows approximately the same amount of energy being consumed each month. After several years, it changes to a pattern where energy usage is higher during the summer months before returning to the usual amount. Possible Directions  I've wondered whether I can continue to compare whole time series, but split them and consider them as a separate series if the pattern changes considerably. However, to do this I'd need to be able to detect such changes. Also, I just don't know if this is a suitable way or working with the data. I've also considered splitting the data and considering it as many separate time series. For instance, I could consider every day/meter combination as a separate series. However, I'd then need to do similarly if I wanted to consider the weekly/monthly/yearly patterns. I think this would work, but it's potentially quite onerous and I'd hate to go down this path if there's a better way that I'm missing.  Further Notes These are things that have come up in comments, or things I've thought of due to comments, which might be relevant. I'm putting them here so people don't have to read through everything to get relevant information.  I'm working in Python, but have rpy for those places where R is more suitable. I'm not necessarily looking for a Python answer though - if someone has a practical answer of what should be done I'm happy to figure out implementation details myself. I have a lot of working &quot;rough draft&quot; code - I've done some DTW runs, I've done a couple of different types of clustering, etc. I think I largely understand the direction I'm taking, and what I'm really looking for is related to how I process my data before finding distances, running clustering, etc. Given this, I suspect the answer would be the same whether the distances between series are calculated via DTW or a simpler Euclidean Distance (ED). I have found these papers especially informative on time series and DTW and they may be helpful if some background is needed to the topic area: What are PPAs and how do I use them? I keep reading about  ('PPAs') and people answer questions with a link to a PPA. What's the best way to use these?     There are multiple valid answers for this question spanning over several versions of Ubuntu. For your convenience, an index of each is below. Accessing localhost (xampp) from another computer over LAN network - how to? I have just set up a wi-fi network at home. I have all my files on my desktop computer (192.168.1.56) and want to access localhost over there from another computer (192.168.1.2).  On my desktop I can access localhost through the normal . Apache is running on port 80 as usual.  Exactly what do I have to do to achieve this? There is documentation on the net but they either don't work or are too fragment and confusing to understand.  I think I have to make changes to my apache's httpd.conf file and the hosts file. Any ideas as to what changes to make? $A_4$ has no subgroup of order $6$? Can a kind algebraist offer an improvement to this sketch of a proof?     Show that $A_4$ has no subgroup of order 6.     Note, $|A_4|= 4!/2 =12$. Suppose $A_4&gt;H, |H|=6$. Then $|A_4/H| = [A_4:H]=2$. So $H \vartriangleleft A_4$ so consider the homomorphism $\pi : A_4 \rightarrow A_4/H$ let $x \in A_4$ with $|x|=3$ (i.e. in a 3-cycle) then 3 divides $|\pi(x)|$ so as $|A_4/H|=2$  we have $|\pi(x)|$ divides 2 so $\pi(x) = e_H$ so $x \in H$ so $H$ contains all 3-cycles but $A_4$ has $8$ $3$-cycles $8&gt;6$, $A_4$ has no subgroup of order 6. How can aperture be f/11 on a lens with an aperture range designation of 3.5-5.6? What is so called meta-game in StarCraft 2?    What other games have this meta-game? I want to programmatically create a site using custom web templates in sharepoint 2010.  In 2007 I used to get a   SPWebTemplate template = site.GetCustomWebTemplates(LCID)[number];   and used this SPWebTemplate in  SPWeb newSite = web.Webs.Add(url, title, description, LCID, template, true, false);   This worked quite well for 2007. But in 2010 the site templates are saved into the solution store  SPSite.Solutions   which only returns SPUserSolution objects and not SPWebTemplates.  So my question is: How can I programmatically create sites using the site templates from the solution store.    UPDATE: I tried to use  SPWeb newSite = web.Webs.Add(url, title, desc, LCID, templateName, true, false);   where templateName is a string like '{Template-GUID}#TemplateName', but it still does not work. It throws the following error:  Critical error: File or arguments not valid for site template '{4a2d8952-a0af-49a6-8f55-46a59c8d68a2}#CustomerSiteTemplate'. Parameter name: WebTemplate    Any other ideas how to create a site based on a SPWebTemplate? I am having a problem with permissions on a Linux server. I am used to BSD. When a directory is owned by a group the user who owns it isn't in such as www-data, files created in it will be owned by that group. This is important because I want files to be readable by the webserver (which I will not run as root) but so a user can still put new files in the directory. I can't put the users in www-data because then they can read every other users websites.   I want the webserver to read all websites, I want users to be able to change their own.  The permissions are set like this on the folders at the moment....  drwxr-x--- 3 john www-data 4096 Feb 17 21:27 john   It is standard behavior on BSD for permissions to work this way. How do I get Linux to do this? Proof of $(A - B) - C = A - (B \cup C)$ I have several of these types of problems, and it would be great if I can get some help on one so I have a guide on how I can solve these.  I tried asking another problem, but it turned out to be a special case problem, so hopefully this one works out normally.   The question is:  Prove $(A - B) - C = A - (B \cup C)$  I know I must prove both sides are not equivalent to each other to complete this proof. Here's my shot: We start with left side.   if $x \in C$, then $x \notin A$ and $x \in B$. So $x \in (B \cup C)$ So $A - (B \cup C)$   Is this the right idea? Should I then reverse the proof to prove it the other way around, or is that unnecessary? Should it be more formal?  Thanks! Which files shouldn't be checked in into version control in Android Studio