I have looked at many questions regarding this but none have solved my issue. I am using a template to write my thesis and want to change the size of my paper but am unable to do so with the command:     \documentclass[letterpaper, 12pt, oneside]{Thesis}   I have tried the following as well     \usepackage[letterpaper]{geometry}   but that ends up changing the formatting of the document and puts all the written content to the top left hand of the page.
Quick question to anyone who has used this LaTeX template:    Any ideas on how to change the left margin to get more words onto one page?
Intuition for why the sum of Bernoulli trials is a sufficient statistic via cancellations on numerator and denominator? Suppose that $X_1, \ldots, X_n$ are iid Bernoulli trials with parameter $p$, and that $Y = \sum_{i=1}^nX_i$. Then, we have that $Y$ is a sufficient statistic by the following condensed proof:  $$ P(X_1 = x_1,  ... , X_n = x_n |Y = y) = \frac{p^y(1-p)^{n-y}}{\binom{n}{y}  p^y(1-p)^{n-y}} =\frac{1}{\binom{n}{y}}   \text{ if } \sum_{i=1}^{n}x_i = y $$  I am trying to see why this is the case. My reasoning is that there is some cancellation property on top and bottom that "kills" off the parameter $p$. In that whatever is on top through $p$ is perfectly matched by whatever is on the bottom minus scaling factors (in this case $\binom{n}{y}^{-1}$).   However, I am wondering what the deeper meaning behind this is, that the numerator of the joint distribution of the data and the sufficient statistic has its EXACT form on the bottom, except for constants which are only multiplicative (to facilitate cancellations). Am I onto something bigger and deeper here? I'm not too sure how to describe the effect that I'm going for or what it is even called.  Thus, I'm having some trouble finding any help through Google.    I want to accomplish something like this "SLOPED" text below, but have the bottoms of the letters follow the slope as well instead of being horizontal.    I have tried using the free transform tool, skewing, and using perspective, but I don't like the effect they are resulting in.  All of the tools that I just mentioned result in the appearance of the word being angled away from the viewer (perspective).  I want more of this style effect, whereas the letters are not skewed horizontally, but scaled evenly along a path that I lay out.  What is the name of this text effect?  Can anyone point me in the right direction to a tutorial or know how to accomplish this themselves?  I know that I could go through and do this letter by letter, but I was really hoping to find an easier method.  EDIT I have removed many elements of my design and quickly threw some sample text in it, but this should give you an idea of what I am trying to accomplish.  I want a mixture of the above and below effects. Normality of dependent variable = normality of residuals? This issue seems to rear its ugly head all the time, and I'm trying to decapitate it for my own understanding of statistics (and sanity!).   The assumptions of general linear models (t-test, ANOVA, regression etc.) include the "assumption of normality", but I have found this is rarely described clearly.   I often come across statistics textbooks / manuals / etc. simply stating that the "assumption of normality" applies to each group (i.e., categorical X variables), and we should we examining departures from normality for each group.   Questions:     does the assumption refer to the values of Y or the residuals of Y?  for a particular group, is it possible to have a strongly non-normal distribution of Y values (e.g., skewed) BUT an approximately (or at least more normal) distribution of residuals of Y?   Other sources describe that the assumption pertains to the residuals of the model (in cases where there are groups, e.g. t-tests / ANOVA), and we should be examining departures of normality of these residuals (i.e., only one Q-Q plot/test to run).  does normality of residuals for the model imply normality of residuals for the groups? In other words, should we just examine the model residuals (contrary to instructions in many texts)?  To put this in a context, consider this hypothetical example:   I want to compare tree height (Y) between two populations (X).   In one population the distribution of Y is strongly right-skewed (i.e., most trees short, very few tall), while the other is virtually normal  Height is higher overall in the normally distributed population (suggesting there may be a 'real' difference). Transformation of the data does not substantially improve the distribution of the first    population.  Firstly, is it valid to compare the groups given the radically different height distributions? How do I approach the "assumption of normality" here? Recall height in one population is not normally distributed. Do I examine residuals for both populations separately OR residuals for the model (t-test)?     Please refer to questions by number in replies, experience has shown me people get lost or sidetracked easily (especially me!). Keep in mind I am not a statistician; though I have a reasonably conceptual (i.e., not technical!) understanding of statistics.  P.S., I have searched the archives and read the following threads which have not cemented my understanding: Why is . not in the path by default? On UNIX-like systems over the years (most relevantly to me, Linux), I've noticed that . (current dir) is never in the $PATH by default.  Why is this?  I recall reading years ago that it was a security problem, but the article I read didn't explain what exactly the problem was.  Is it because someone could leave a malicious version of ls or cp in a directory, and I'd end up running it without realizing it was there? I recently setup a new computer for my parents with windows 10 home. I made two local accounts for them - no microsoft accounts. I also would like to keep them without a password. Problem is now that windows automatically signs in with the last used account. No lock/login screen.  I tried a number of answers from similar questions here but none worked. Since it's a home version there are no group policies and the method using task scheduler does not work because accounts with no password are not allowed to create such tasks.  Are there other options to force windows to show a user list on startup without setting passwords for the accounts? Why is a black hole black? TV series with pull out phone screens and pink/purple space ships I’m looking for a TV show where an alien race comes to Earth and sets up big purple/pink cylindrical or cone shaped spaceships in various cities around the world. The Aliens are not hostile but actually created peace and eliminated hunger on Earth.    I believe the aliens had some human features and were wise and calm the main actor had a phone with a pull out screen I believe the main actor worked for or with the aliens I believe that in the last episode some humans and aliens go into some kind of pods and perhaps leave Earth? one of the space ships was located in a major US city. Maybe Washington DC or another East Coast city   Could someone please tell me what TV series this is? I have been searching everywhere and cannot find it. Thanks! What is the name of a squircle with three, five, six or more corners? I know that the second shape is a squircle, but what are the other shapes called? Is there an actual name for them?    The shapes do not simply have rounded corners, but the sides have a "circularity". Here is a triangle with rounded corners next to the shape that I do not know the name of:    "Trircle", "Triarcle", and "Pentircle" do not seem to be used for them, at least Google's image search does not provide any results. By integration by parts and the substitution $x = \sin t$ we can easily calculate the integral $\int_{0}^{1} \ln (x+ \sqrt{1-x^2})dx$ which equals to $\sqrt{2} \ln (\sqrt{2} +1) -1.$ I’ve tried to use the same substitution $x = \sin t$ to calculate the integral $ \int_{0}^{1} \frac {\ln (x+ \sqrt{1-x^2})}{x}dx,$ which becomes $$ \int_{0}^{\frac {\pi}{2}} \frac {\ln \sin (t+ \frac {\pi}{4})}{\sin t}dt$$ It seems difficult to solve the particular integral. Any help? I have a Dell Inspiron 1525 laptop and I am planning on purchasing a mac mini, new version , I am tight on money for a while and want to use my current laptop screen as monitor for mac mini, I just want to know if it is at all possible to do, I have windows 7 and ubuntu 11.04 installed in my laptop, and I don't really care if need to wipe them out, or purchasing a monitos is the only option left, also I am planning to use it for coding and stuff, so VNC is probably not a good choice. Is there console mode in Mac OS X? Given a string of JSON data, how can I safely turn that string into a JavaScript object?  Obviously I can do this unsafely with something like:  var obj = eval("(" + json + ')');   but that leaves me vulnerable to the JSON string containing other code, which it seems very dangerous to simply eval. SQLite - UPSERT *not* INSERT or REPLACE Is there some clever way to do this in SQLite that I have not thought of? Basically I want to update three out of four columns if the record exists, If it does not exists I want to INSERT the record with the default (NUL) value for the fourth column. The ID is a primary key so there will only ever be one record to UPSERT. (I am trying to avoid the overhead of SELECT in order to determine if I need to UPDATE or INSERT obviously) Suggestions?  I cannot confirm that Syntax on the SQLite site for TABLE CREATE. I have not built a demo to test it, but it doesn't seem to be supported. If it was, I have three columns so it would actually look like: CREATE TABLE table1(      id INTEGER PRIMARY KEY ON CONFLICT REPLACE,      Blob1 BLOB ON CONFLICT REPLACE,      Blob2 BLOB ON CONFLICT REPLACE,      Blob3 BLOB  );  but the first two blobs will not cause a conflict, only the ID would So I assume Blob1 and Blob2 would not be replaced (as desired)  UPDATEs in SQLite when binding data are a complete transaction, meaning Each sent row to be updated requires:  Prepare/Bind/Step/Finalize statements unlike the INSERT which allows the use of the reset function The life of a statement object goes something like this:  Create the object using sqlite3_prepare_v2() Bind values to host parameters using sqlite3_bind_ interfaces. Run the SQL by calling sqlite3_step() Reset the statement using sqlite3_reset() then go back to step 2 and repeat. Destroy the statement object using sqlite3_finalize().  UPDATE I am guessing is slow compared to INSERT, but how does it compare to SELECT using the Primary key? Perhaps I should use the select to read the 4th column (Blob3) and then use REPLACE to write a new record blending the original 4th Column with the new data for the first 3 columns? Can multiple render systems be used? Can I combine extension tubes and macro filters at once to give better macros? What is the strict aliasing rule? How can I break an align environment for a paragraph? I would like to have two displayed equations, broken by a short paragraph, but with aligned equal signs (as if using the align environment).  Is there some way to "break" the align environment temporarily? In what order should you do linear regression diagnostics? Our high-school teacher told us that the Earth pulls us with some force $F$ and we pull the Earth with the same force $F$. Within Newtonian physics this is true because of , but let’s consider . My mass is small; so I don’t warp space-time much. But Earth’s large mass warps space-time to a far greater extent.  So do I pull Earth with the same force it pulls me? If yes, how? Transaction log reported full but is not