Calculating total score for a scale including polytomous and dichotomous items
Can a dichotomous variable (yes/no) be merged with a Likert measure (1,2,3,4) using z scores?
How do candles and wicks work? Identity for convolution of central binomial coefficients: $\sum\limits_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$ It's not difficult to show that  $$(1-z^2)^{-1/2}=\sum_{n=0}^\infty \binom{2n}{n}2^{-2n}z^{2n}$$  On the other hand, we have $(1-z^2)^{-1}=\sum z^{2n}$.  Squaring the first power series and comparing terms gives us  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}2^{-2n}=1$$  that is,  $$\sum_{k=0}^n \binom{2k}{k}\binom{2(n-k)}{n-k}=2^{2n}$$  My question: is there a more direct, combinatorial proof of this identity?  I've been racking my brains trying to come up with one but I'm not having much success. With lots of guides and setup variations all over the internet, I find it confusing which is which to really follow. Normally, in Windows 8 my setup would be install everything in the HDD and use Intel Smart Response for a speedy setup. However as I am new to Linux I really don't know what to do.  My ideal setup would be something similar to this, but I know for a fact that IRST is not available in Linux so what I intend to do is keep the OS files in the SSD instead and keep my media on the larger HDD. A step by step procedure would be extremely helpful.     Edit: I want a system running solely on Ubuntu, with the SSD to speed things up but setting it in such a way that it does not hasten its lifespan.    # /etc/fstab: static file system information.  # # Use 'blkid' to print the universally unique identifier for a  # device; this may be used with UUID= as a more robust way to name devices  # that works even if disks are added and removed. See fstab(5).  #  # &lt;file system&gt; &lt;mount point&gt; &lt;type&gt; &lt;options&gt; &lt;dump&gt; &lt;pass&gt;  # / was on /dev/sda1 during installation  UUID=80289460-5983-4349-8afc-6f3119938ee9 / ext4 errors=remount-ro 0 1   # /files was on /dev/sdb5 during installation  UUID=c1678c88-5100-41bc-8090-7887f1622c7f /files ext4 defaults 0 2   # swap was on /dev/sdb6 during installation  UUID=608e3ec2-c76e-4657-af6d-80793b5f50f6 none swap sw 0 0 I am wondering if there is a modifier or tool that will essentially undo a subsurf or subdivide command. How do I improve boot speed? Question about probable fixed use of "what do you do?" and "how do you do?" Do we always have to use the question how do you do? fixed in greeting people? Can we ask it in other situations rather than greetings? Like when we are wondering how someone is doing the given task.  Do we always have to use the question what do you do? for asking about sojeone's job? Can we use it sonetimes instead of ** what are you doing?** Suppose $ \alpha, \beta&gt;0 $. Compute:   $$ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $$   Here is what I do: $$\begin{align} \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx &amp;= \int_{0}^{\infty}dx\int_{\alpha}^{\beta}\sin (yx)dy\\ &amp;=\int_{\alpha}^{\beta}dy\int_{0}^{\infty}\sin(yx)dx\\ &amp; \\ &amp;   \qquad\text{let $ yx=u $}\\ &amp; \\ &amp;=\int_{\alpha}^{\beta}\frac{1}{y}dy\int_0^{\infty}\sin u du\\ &amp;=\int_{\alpha}^{\beta}\frac{1}{y}dy\left( -\cos u|_{\infty}+\cos u|_0 \right)\\ &amp;=\log\frac{\beta}{\alpha}(-\cos(\infty)+1)\\ &amp;=\log\frac{\beta}{\alpha}-\cos(\infty)\log\frac{\beta}{\alpha} \end{align}$$  But $ \cos(\infty) $ does not exist right? Does it mean the integral actually diverse?  Edit: The question comes from   Who can point out my mistake in the above deduction? What home printer would allow for exact alignment of front and back? Note: I'm not a graphic designer, but this seemed like the most relevant place to post. Feel free to send me off somewhere else if I'm not in the right place.  I would like to make some notebooks with double-sided grid paper that I've already designed, but my printer seems like it doesn't allow for absolutely exact alignment. Even if one side prints nice and straight, the other side will be slightly skewed left to right by one to two millimeters, which I read from an earlier post is a pretty reasonable variance for a home printer. So I suspect it's not possible to get both sides completely aligned on this printer – but if I'm wrong, please let me know how.  What kind of printer would allow for absolutely exact alignment? Is there any difference between inkjet and laser in this regard, or a more expensive printer versus a cheaper one? How do I create a new object using Python in Blender 2.80? As part of an existing add-on, I'm trying to create an object and add it to the scene using Python. I followed a Blender Cookbook tutorial found here: . I use the following code to do so:  emptyMesh = bpy.data.meshes.new('emptyMesh') theObj = bpy.data.objects.new("object_name", emptyMesh) bpy.context.scene.objects.link(theObj)   But I get the following error when I try to link theObj to the scene objects:  AttributeError: 'bpy_prop_collection' object has no attribute 'link'   This works just fine in Blender 2.76-2.79, but doesn't work in the 2.80 test build I downloaded. Was there a change to the Python API? Or is this maybe a bug in the test build? UK visa: unsigned application form There is this puzzling thing that is called : paradoxically, warm (35°C) water freezes faster than cold (5°C) water.  As a physisist, I've been asked about it several times already. And I have no definite answer to that, apart from the standard: "there are many things that can influence it".  So, does anyone knows about the status or progress on that effect? Any recent reviews, publications or other references? Given that $\displaystyle{a+b\sqrt[3]{2} +c\sqrt[3]{4} =0}$, where $a,b,c$ are integers. Show $a=b=c=0$  Do I use modular arithmetic? Which colors make you hungry I am working on a new brand, which is all about food.   What colors should we use for the logo and website?   I keep reading that red makes you hungry, but i would like to stay away from that color. All of our competitors must have read the same articles. Prove that $\int_0^{\infty} \frac{\sin x}{x^p}\, dx$ converges for $0<p<2$ What is the difference between .pem, .csr, .key and .crt and other such file extensions? I'm new to SSL / TLS and I want to work with the OpenSSL toolkit.  I don't know what .pem and .csr stands for?  I do know that .key is the private key and .crt is the public key. Video lectures on graduate level Classical Electrodynamics This is a rather broad question. Does anyone know of good video lectures for graduate level classical electrodynamics? Process management and high technology weapon. Novel name and author? My neighbor has asked me help with his laptop, an HP with lost power-on password. I tried inserting an Ubuntu cd to format the partition, but well... it doesn't even get there. Any ideas? Is "TABLESAMPLE BERNOULLI(1)" not very random at all? Unintentional mouse movements, am I paranoid?