Logistic regression model fit assessment
Evaluating logistic regression and interpretation of Hosmer-Lemeshow Goodness of Fit
Assume f is a bounded continuous function on $\mathbf{R}$ and $X$ is a random variable with distribution $F$.  Assume for all $x \in \mathbf{R}$ that  $$ f(x) = \int_\mathbf{R}f(x+y)F(dy) $$  Please help conclude that $f(x+s) = f(x)$ where $s$ is any value in the support of $F$.  The hints that I have come across are to use Martingale theory and consider $\{ X_n\}$ to be i.i.d. with distribution $F$ and make a martingale with some function of $S_n = \sum_{j=1}^nX_j$.    Thanks! CakePHP View including other views I have a CakePHP application that in some moment will show a view with product media (pictures or videos) I want to know if, there is someway to include another view that threats the video or threats the pictures, depending on a flag. I want to use those "small views" to several other purposes, so It should be "like" a cake component, for reutilization.  What you guys suggest to use to be in Cake conventions (and not using a raw include('') command) What are tag synonyms and merged tags? How do they work? Can't find Corruption Why "be king", not "be a king"? I've heard people say "be king" (as in "I can't wait to be king") in movies and TV. Why don't they say "be a king"? Which is correct? Changing capitalization of filenames in Git Mclaurins with $e^{\sin(x)}$ To evaluate $e^{\sin(x)}$ I use the standard series $e^t$ and $\sin(t)$, combining them gives me:  $e^t = 1+t+\dfrac{t^2}{2!}+\dfrac{t^3}{3!}+\dfrac{t^4}{4!}+O(t^5)$  $\sin(t) = t-\dfrac{t^3}{3!}+O(t^5)$  $\therefore e^{\sin(x)} = 1+\sin(x)+\dfrac{\sin^2(x)}{2!}+\cdots+O(x^5)$  $\iff e^{\sin(x)}=1+\left(x-\dfrac{x^3}{6}\right)+\dfrac{\left(x-\frac{x^3}{6}\right)^2}{2}+\dfrac{x^3}{6}+O(x^5) = 1+x +\dfrac{x^2}{2}-\dfrac{x^4}{6} + O(x^5)$  In the last step, I only evaluate up to $\sin^3x$ term, everything above has a grade equal to or greater than $x^5$  However, I'm wrong. According to Wolfram, the series expansion for $e^{\sin x} = 1+x+\dfrac{x^2}{2}-\dfrac{x^4}{8}+O(x^5)$.  What did I do wrong? I can't seem to find what or where. Find the sum of finite series $S=\sum_{k=1}^{2015}{(-1)^{\frac{k(k+1)}{2}}}k$ the least possible value for :$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $ If we know that for every $a,b,c&gt;0$ ,how we can find  the least possible value for :  $$ \lfloor \frac{a+b}{c}\rfloor +\lfloor \frac{b+c}{a} \rfloor+\lfloor \frac{c+a}{b} \rfloor $$ Bibliography in Texmaker USB flash drive autorun How to install Google Chrome How do you install Google Chrome on Ubuntu? Is there a way to get the raw SQL string executed when calling PDOStatement::execute() on a prepared statement? For debugging purposes this would be extremely useful. How would you implement an LRU cache in Java? Please don't say EHCache or OSCache, etc. Assume for purposes of this question that I want to implement my own using just the SDK (learning by doing). Given that the cache will be used in a multithreaded environment, which datastructures would you use? I've already implemented one using  and , but I'm curious if any of the new concurrent collections would be better candidates.  UPDATE: I was just reading through  when I found this nugget:     If you need constant-time access and want to maintain the insertion order, you can't do better than a LinkedHashMap, a truly wonderful data structure. The only way it could possibly be more wonderful is if there were a concurrent version. But alas.   I was thinking almost exactly the same thing before I went with the LinkedHashMap + Collections#synchronizedMap implementation I mentioned above. Nice to know I hadn't just overlooked something.  Based on the answers so far, it sounds like my best bet for a highly concurrent LRU would be to extend  using some of the same logic that LinkedHashMap uses. Area is calculating wrong using $area in field calculator (QGIS 2.8.1-Wien) Where do I find the maximum node? A lot of people recommend to use the maximum node for glass setup, but I can't find that node. Nothing comes up when I search for it.  Where do I find it? My 8 year old son won't fall asleep We put him to bed at 9pm and he stays up til 1am or later. When I go to check on him he is always playing with his hands and sometimes talking. I ask him why he is awake and not trying to sleep and he says it's because he just wants to play. He never comes to tell us that he is having a hard time sleeping or that there is anything wrong. The weird thing is that he used to be the first one to fall asleep out of 3 boys and the staying up started a few months ago. He does this every night and on top of keeping us awake, he is now waking up his brothers.   About a month or so ago, we decided to punish him by grounding him from video games. He doesn't want to be grounded, but he still keeps doing it. Nothing we do seems to be helping and it seems to be getting worse. I have talked to him about why it is so important to get enough sleep and why it's even more important for kids. He also gets plenty of exercise and time to play during the day.   I'm really starting to wonder if he is doing it just to be defiant. If anyone has any suggestions I would greatly appreciate it.  The problem is that he is being disruptive to everyone in the house and it has been EVERY night for the last 3 months.   He is tired and emotional during the day, and it is causing his brothers to be tired during the day while they are at school.   Because he is tired during the day he doesn't really want to be as active as he used to be. However, I do still encourage him to be active. We have always had a bedtime routine. We have asked him many different times if he is just having trouble sleeping, if he is uncomfortable, and if there is something wrong. He always tells us that he just wants to play.   At the beginning of all this he told me that he wants to be the one to decide when he goes to sleep and when he wakes up. Which is why I would even ask if it was out of defiance.   We really didn't want to get to the point of punishing him, but nothing else seemed to help and it was only after he started keeping his brothers awake.   It's not like we haven't asked him what he thinks would help or what would help him sleep better. He ALWAYS says that he just WANTS to stay up and play because it is fun. We know it is important for him to get enough sleep, and I'm worried because I don't think he is (and he's preventing the rest of us from getting enough, too). How to integrate OpenCV Manager in Android App Consider the closed interval $[0,1]$, there is $\frac{2}{3} \in [0,1]$ where $p=2$ and $q=3$. Similarly consider $[2,3]$, one can have $\frac{5}{2} \in [2,3]$ where $p=5$ and $q=2$. Does every interval of the form $[a,b]$, where $a,b \in \mathbb{R}$ contain a rational of this kind. If yes, how can we prove it? Is it possible to shutdown remote Computers without inputing the password? I used the following bash to shutdown remote computers,but for each computer,I must input the password for it.Is it possible to input the password Automatically?   #!/bin/bash  ssh -t root@192.168.1.11 "sudo poweroff" ssh -t root@192.168.1.12 "sudo poweroff" ssh -t root@192.168.1.13 "sudo poweroff" ssh -t root@192.168.1.14 "sudo poweroff" ssh -t root@192.168.1.15 "sudo poweroff" ssh -t root@192.168.1.16 "sudo poweroff" ssh -t root@192.168.1.17 "sudo poweroff" ssh -t root@192.168.1.18 "sudo poweroff" ssh -t root@192.168.1.19 "sudo poweroff" ssh -t root@192.168.1.20 "sudo poweroff" ssh -t root@192.168.1.21 "sudo poweroff" ssh -t root@192.168.1.22 "sudo poweroff" ssh -t root@192.168.1.23 "sudo poweroff" ssh -t root@192.168.1.24 "sudo poweroff" ssh -t root@192.168.1.25 "sudo poweroff" ssh -t root@192.168.1.26 "sudo poweroff"