says  Enchant Creature Creatures you control that are enchanted get +1/+1 If a creature you control that's enchanted would die,  return it to it's owners hand instead.   Is that a +1/+1 counter? Or is it just a modification to the P/T?  Also, given the language it reads as if it means to say any creature enchanted by any enchantment. Correct?
Is a +1/+1 counter I get from, say Unleash or Undying different than +1/+1 from something like  or ?
I am unable to find the bias of the sample variance estimator in this problem. Unfortunately I keep coming up with   Question: Suppose that the true linear model is   $y = X_1\beta_1 + X_2\beta_2 + e$,   where $e \sim MVN(0,\sigma^2 I)$, $X_1: N \times p_1, \beta_1: p_1 \times 1, X_2: N \times p_2, \beta_2: p_2 \times 1$. But we wrongly fit the model  $y = X_1\beta_1+e$ and calculate the estimators of $\beta_1$ and $\sigma^2$ as:  $\hat{\beta}_1 = (X_1'X_1)^{-1}X_1'y$,  $s^2 = \large \frac{y'[I-X_1(X_1'X_1)^{-1}X_1']y}{N-p_1}$.  (a) Show that, in general, $\hat{\beta}_1$ is a biased estimator with  Bias$(\hat{\beta}_1) = (X_1'X_1)^{-1}X_1'X_2\hat{\beta}_2$  Under what condition on $X_1$ and $X_2$ is $\hat{\beta}_1$ unbiased?  (b) Show that, in general, $s^2$ is a biased estimator with   Bias$(s^2) = \frac{1}{N-p_1}\beta_2'X_2'[I-X_1(X_1'X_1)^{-1}X_1']X_2\beta_2$  Is the bias positive or negative? Under what condition on $\beta_2$ is $s^2$ unbiased?  Attempt:  For part (a):  Bias$(\hat{\beta}_1) = E((X_1'X_1)^{-1}X_1'y - \beta_1)$  $\hspace{15mm}= (X_1'X_1)^{-1}X_1'E(y) - \beta_1$  $\hspace{15mm}= (X_1'X_1)^{-1}X_1'(X_1\beta_1 + X_2\beta_2) - \beta_1$  $\hspace{15mm}= (X_1'X_1)^{-1}X_1'X_1\beta_1 + (X_1'X_1)^{-1}X_1'X_2\beta_2) - \beta_1$  $\hspace{15mm}= I\beta_1 + (X_1'X_1)^{-1}X_1'X_2\beta_2 - \beta_1$  $\hspace{15mm}= \beta_1 + (X_1'X_1)^{-1}X_1'X_2\beta_2 - \beta_1$  $\hspace{15mm}= (X_1'X_1)^{-1}X_1'X_2\beta_2$  If $X_1$ and $X_2$ are orthogonal, then $\hat{\beta}_1$ is unbiased.  For part (b), I am unable to figure out how to derive:  Bias$(s^2) = \frac{1}{N-p_1}\beta_2'X_2'[I-X_1(X_1'X_1)^{-1}X_1']X_2\beta_2$  I can get   $\frac{1}{N-p_1}\beta_1'X_1'+\beta_2'X_2'[I-X_1(X_1'X_1)^{-1}X_1']X_1\beta_1+X_2\beta_2$  after taking the expectation of y on both sides.   Any help would be much appreciated. Prove $\sup(f+g) \le \sup f + \sup g$ Suppose $D$ is a nonempty bounded subset of reals. Let $f:D \to \mathbb R$ and $g:D \to \mathbb R$. Define $(f+g)(x)=f(x)+g(x)$. Prove $\sup(f+g)(D) \le \sup f(D) + \sup g(D)$ (also prove that $\sup (f+g)$ exists).   I understand why this is the case, just not how to prove it. Left side is pretty much $\sup  (f(x)+g(x))$ and right side is $\sup (f(x) + g(y))$ for $x,\,y \in D$. Basically $f+g$ has to use the same variable and $f(D)+g(D)$ use different ones. But I don't know how to go about proving this.     The second part of the question is to find a specific example where strict inequality holds.    Let $D=\{a,b\}$ and $f: a \to 1,\, b\to 0, \,g: a \to 0,\, b\to 1$. $\sup f(D) = 1,\, \sup g(D) = 1,\, \sup f(D) + \sup g(D) = 2.$ $\sup (f+g)(D) = 1$ (if we choose a, $f+g = 1+0,\, b,\, f+g=0+1$). Am I Using JDBC Connection Pooling? To show for following sequence $\lim_{n \to \infty} a_n = 0$ where $a_n$ = $1.3.5 ... (2n-1)\over 2.4.6...(2n)$ Parsing XML, JSON, and newer data file formats in UNIX using command line utilities The Unix environment has some excellent tools for parsing text in various forms. However, of late, the data is not in the traditional (historical) formats (CSV, TSV, record-based or some other delimiter-based) it used to be before. Data these days is exchanged in structured formats like XML/JSON.  I know there are some good tools like sed, awk and Perl which can chew down nearly any form of data out there. However, to work with this sort of structured data, often one has to write a complete program, and, given the little time available to extract information, one has to sit down and figure out the whole logic of what one wants to query and put it down programmatically. Sometimes this is not OK – basically because the information extracted from those files acts as inputs for further work; also because of the time it takes to search for the appropriate solution and code it up. A command line tool is needed with sufficient switches to find, query and dump data.  I'm looking for tools that take a XML/JSON or other forms of structured data and dump it into other formats like csv, etc., so that from there one could use other commands to get any information out of it.  Are there any command line utilities you know of which do this kind of a job? Are there already awk/Perl scripts available to this? Is Double-Annotating HREFLANG always alright? What if I remove one of them? Text formatting now allowed in comments (List of proven and disproven abilities) What is the likelihood of ever discovering the graviton? How would one look for and confirm existence of a graviton?  Someone was speaking to me about perhaps one day discovering the graviton, but to me it seems unlikely, although I'm young and essentially quite naive, so am coming to you physicists to ask    What actually is the likelihood of finding it?  How would we find it? Is it possible to perform a power analysis for the Kruskal-Wallis and Mann-Whitney U test? If yes, are there any R packages/functions that perform it? PostgreSQL: running count of rows for a query 'by minute' How to prove or disprove statements about sets Prove or disprove:  The set: $\{ \emptyset\}^{\Bbb N}$ has only one element.  The set $\emptyset^{\Bbb N}$ is empty.    I'm pretty sure both are true, for 1. all the natural numbers go to the empty set and that is the only element. Where as 2. all the natural numbers go to nothing so that's why it's empty. (Same as $ {\Bbb N}^{\emptyset} $ nothing goes to something is nothing (I think)). The problem is I have no idea how to show this so advice would be appreciated.  Edit: My defintion of a function is: $f:B\to A$ if  $(a_1,b),(a_2,b)\in f \ \Rightarrow \ a_1=a_2$ So for 2. I can simply say that: $(1,\emptyset),(2,\emptyset)\in f \Rightarrow a_1\neq a_2$  ? Pacman option to assume "yes" to every question? When installing software in debian systems we can put something like this:   sudo apt-get install -y chromium-browser  that way the installation occurs automatically, whitout asking to confirm installation [Y/n]. Can i do the same with pacman? Is const_cast safe? I can't find much information on const_cast.  The only info I could find (on Stack Overflow) is:     The const_cast&lt;&gt;() is used to add/remove const(ness) (or volatile-ness) of a variable.   This makes me nervous.  Could using a const_cast cause unexpected behavior?  If so, what?  Alternatively, when is it okay to use const_cast? Maybe a stupid question but how can I tell if I have a static IP address or a dynamic IP address? Running Fedora-13 Physically Identify the failed hard drive For example, "dude," "man," "buddy," "pal," etc, when used to stand in for someone's name.  "Hey, pal, how's it going?"  Is there a word for terms like these?  Or is "colloquialism" as close as we can get? If $\alpha$ is an algebraic element and $L \subset K$ are both field, does the polynomial ring $L[\alpha]$ is also a field?  I am trying to prove that the ring of fraction $L(\alpha)$ is equal to $L[\alpha]$. To do this, I use an exercise done in class : Let $K$ a field, $\alpha \in K$ and $L$ a subfield of $K$. Then $L(\alpha)$ is the smallest subfield of $K$ containing $L$ and $\alpha$.  Is anyone could help me? My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant.   All the regression assumptions are met. No multicollinearity was found. Correlations among all predictors are all less than 0.60.   What else might be the cause of the insignificant predictors? iCloud has sucked up all my laptop's files - can you transfer files directly from iCloud to Google Drive? I'm trying to disconnect my macbook from iCloud, as it's been creating some problems.  I was told by an Apple Support employee that doing so is only recommended once you've backed up everything from your Mac somewhere, to ensure you don't lose any files - so my goal is to upload everything to Google Drive before messing with my laptop's iCloud settings. The problem is, almost none of the projects that I want to back up to Google Drive are truly on my laptop - instead I mostly just have folders full of file names, which are placeholders for the real files that have been sucked into iCloud. This means I have to re-download everything to my computer before uploading it all to Google Drive. Another crucial piece of information is that I only have 1 GB of storage left on my macbook, which prevents me from re-downloading any complete projects/folders at a time. So unfortunately my current method is this: downloading 1-5 files at a time, uploading these few things to Google Drive, deleting the copies from my laptop and trash, repeat (thousands of times). So, I was wondering if anyone could offer any alternative methods for uploading stuff to Google Drive in this situation - for example, is there a way to transfer files directly from iCloud to Google Drive without having to download them to my laptop first? I should probably mention that I've scoured my laptop for duplicated files and applications I no longer use, make sure to empty my trash regularly, etc (I also asked Apple Support to help me make sure I wasn't missing out on any other ways to maximize storage space). The most obvious culprit of my lack of space is the massive 150 GB iCloud folder on my laptop, which appears to contain duplicates of everything on my computer. I can't seem to do anything about it until I've disconnected from iCloud itself (its reasons for existence are unclear to me in the first place...but that's beside the point lol). Problem. Assume that $U$ is an open and connected subset of $\mathbb R^2$, and $\gamma :[0,1]\to U$ is a closed curve, which is not null-homotopic in $U$ and not necessarily simple closed. Show that there exists a simple closed curve, which is not null-homotopic in $U$.  I am sure that this is a standard problem, and I am looking for an elegant, if possible, solution or a reference. I have in mind the following sketch of proof:  a. Construct a polygonal closed curve $\tilde\gamma$ which is homotopic with $\gamma$ in $U$.  b. Construct $\tilde\gamma$ so that it intersects itself in finitely many points, and not whole segments.  c. Use induction on the number of self–intersections of $\tilde\gamma$, in order to show that $\tilde\gamma$ is written as a product (in the fundamental group's sense) of simple closed polygonal curves.