If I have  in play and I want to cast , how does Ugin, the Ineffable's static ability interact with paying the cost?  Can I announce I want to cast Ugin's Conjurant for 5 and then only pay 3 mana because Ugin, the Ineffable's static abilit reads "Colorless spells you cast cost 2 less to cast"?
If I play a spell with {X} in the mana cost, and I have a card out that reduces the casting cost by 2 generic mana, what happens to the X? Does it start at -2?  For example: I have  in play. If I play  for just 1 blue mana, do we draw 2 cards?
From the TV Show Krypton, Dru-Zod is the son of Seg-El and Lyta-Zod. In S02E05 'A better yesterday', Lyta-Zod's throat gets slit by Jax-Ur leading to Lyta's death. How is Dru-Zod still alive? Shouldn't he be wiped from existence? Why does Python code use len() function instead of a length method? I know that python has a len() function that is used to determine the size of a string, but I was wondering why it's not a method of the string object.  Update  Ok, I realized I was embarrassingly mistaken. __len__() is actually a method of a string object. It just seems weird to see object oriented code in Python using the len function on string objects. Furthermore, it's also weird to see __len__ as the name instead of just len. Adding GPX files into ArcMap? What is the smoothest route, the easiest user experience, to add  files to ArcMap?  Ideally, I'd like to interact with .gpx with the same facility as .shp, being able drag'n'drop onto the map canvas and so on. Ultimately the results will be feature classes in a file-gdb but shapefile is an acceptable intermediate. Let $X \sim Bin(n,p)$ show that $X/n \nsim Bin()$ Let $X \sim Bin(n,p)$   Part A.  Show that the argument      "Then $X/n \sim Bin()$ with $E[X/n]=p$and $Var[X/n]=pq/n$"    is false.   My book says we can prove this result using a moment generating function. But to me it makes no intuitive sense: We have Bin-distributed RV $X$ and if we rescale it with $1/n$ of course it will be Bin-distributed.  And we know from standard formulas that $E[aX]=aE[X]$ and $Var[aX] = a^2Var[X]$ so I think the argument is correct.   (For full disclosure, the argument we should falsify according to the book is "Let X be a binomial random variable with mean np and variance np(1−p). Show that the ratio X/n also has a binomial distribution with mean p and variance p(1−p)/n." But I think the argument is correct. )    Ok, now I get part A. Here is Part B. Prove it using the moment generating function of $X/n$.   Attempt: I get $$m_X(t)=E[\exp(tX/n)]=(m_X(t))^{1/n}$$ Limit of $\cos(x)/x$ as $x$ approaches $0$ As the title says, I want to show that the limit of  $$\lim_{x\to 0} \frac{\cos(x)}{x}$$  doesn't exist.  Now for that I'd like to show in a formally correct way that   $$\lim_{x\to 0^+} \frac{\cos(x)}{x} = +\infty$$  I'm sure this is right since $\displaystyle\lim_{x\to 0^+} \cos(x) = 1$ and $\displaystyle\lim_{x\to 0^+} x = 0$, but since $\displaystyle\lim_{x\to 0^+} x = 0$ I can't just say:  $$\lim_{x\to 0^+} \frac{\cos(x)}{x} = \frac{1}{\displaystyle\lim_{x\to 0^+} x}$$   Things I tried: expand the fraction and use L'Hospital's rule (This didn't seem to yield results even though I tried quite a few things, should it? If it does, should it always work? It worked for similar problems) and going by the definition of the limit which didn't work for me either.  I'm grateful for any hints for doing this problem and similar problems especially. How to configure lightdm to allow manual logins in Ubuntu 14.04 I used to modify /etc/lightdm/lightdm.conf, adding the line greeter-show-manual-login=true, in order to allow login for hidden users and root.  Now I've just installed the new Ubuntu 14.04 and the file lightdm.conf is no longer located in /etc/lightdm. It's in /etc/init and has been totally modified.  How can I force lightdm login screen to show a field to input a login name? A grim and tragic question perhaps, but I'm curious:  What happens when a person that co-signed on a loan dies? Is the co-signer's estate potentially liable until the loan is paid off, the same as if the co-signer had borrowed the money themselves?  Or, does the responsibility for the loan die with the co-signer?  Does the bank/lender take on that risk? Right-click on Touchpad not working after update to 18.04 LTS Can current be induced in a superconductor? How do I check that multiple keys are in a dict in a single pass? Someone gave me a bunch of envelopes of pizza crust yeast, "specially formulated for pizza crust". The packets also say that no rise time or proofing is needed, and that it's "NOT recommended for bread baking." The ingredients are yeast, enzymes, sorbitan monostearate, l-cysteine, and ascorbic acid. It does provide a recipe for pizza crust, with just mixing and a bit of kneading.   What has actually been done to this yeast to make it work like this? (What are those enzymes?) And is there any way I can use it for other things, or is it really only good for things like pizza crust? How strongly can a 1mo be rocked? My 1 month old baby only seems to quiet down when I vigorously rock her (while I carefully hold her head). Can I cause her some (brain?) damage if I rock her too hard? Why did a Dementor try to take Harry's soul in the train? In "Harry Potter and the Prisoner of Azkaban" - when Harry and his friends were travelling to Hogwarts by train, the train stopped in between and Dementors were searching for Sirius Black. Why did one of the Dementors try to take Harry's soul? "What more" vs "what else" do you need? I am providing you with food, shelter, clothes.      What more do you need   or      what else do you need?   Which one's correct? I feel uncomfortable saying sentences like the following:    "I've a car" instead of "I have a car" "They've a great time" instead of "They have a great time" "He's a pen" instead of "He has a pen" etc   I ask this because I read this sort of thing in a book.  Are they correct? And what is the rule? Can you use such forms in a formal setting? Photoshop To CSS: How do you translate Fill to CSS I have a content box in photoshop with the background color #bc0018 with a 65% opacity and 50% fill.  I am able to translate the backgroundcolor and opacity part to this, but without the 50% fill the backgroundcolor looks different.  .content-box {     background-color: rgba(188, 0, 24, 0.65); }   Any suggestions on also getting the proper "fill" in CSS?  EDIT  I did just divide the opacity by half and it appears to achieve the same effect as a 50% fill. Still, I would love to hear how other people do this? I definitely don't want to create an image just for this.  .content-box {     background-color: rgba(188, 0, 24, 0.325); }   Thanks! What lies beyond the Sedenions Recently, there was some news that said that the researchers at NASA have come across some impossible kind of space engine which does not require any fuel. I have read at a few places like ,  and . They all say that this engine seems to violate the laws of physics including conservation of momentum.  The original paper is .  Is the statement that it violates conservation of momentum true? How to put a brace on the right, not left, to group cases? Should I defragment my SSD?