Interpreting t-values in a categorical regression model: R
What is the meaning of p values and t values in statistical tests?
\hfill \break does not work The set of convergent points of a sequence of continuous functions is Borel Suppose that $f_n$ are continuous.  Prove that $E=\{x\in \mathbb{R}:f_n(x)\text{ is convergent}\}$ is Borel.   My first instinct is to take balls around $\lim_{n\to\infty}f_n(x)$, for each $x$ in $E$, and then show that there has to be some ball small enough so that everything inside that ball is a member of $E$. But this would imply not only that $E$ is Borel, but moreover that it is open, so I don't think that can be right.  Can someone show me how to do this? Last names that are English words with an extra 'e' I noticed that there are a lot of last names that have an 'e' at the end.  The pronunciation usually isn't changed from that of the base word.   Poole Steele Browne Clarke   Why do English words not have the e?  Maybe the answer to this question depends on which came first, pool or poole. Adding Multiple Maps in QGIS Composer? My random variable $X$ is normally distributed with mean $b$ and variance $p$. I defined a new RV, $Y$, such that $Y=1/X$. Does anyone know how to find the mean of $Y$ and $Y^2$? $X_1, X_2, \ldots, X_n$ are $n$ i.i.d. uniform random variables. Let $Y = \min(X_1, X_2,\ldots, X_n)$. Then, what's the expectation of $Y$(i.e., $E(Y)$)?  I have conducted some simulations by Matlab, and the results show that $E(Y)$ may equal to $\frac{1}{n+1}$. Can anyone give a rigorous proof or some hints? Thanks! Probability of complete coupon set in $K$ boxes where a box has $N$ distinct coupons? Say there is a contest to collect a full set of $M$ coupons.  Each box of product has $N$ distinct coupons of the $M$ possible coupons in it, selected uniformly without replacement from the $M$ possible coupons, the same $N$ in number for all boxes.  I'm interested in the probability that after opening $K$ boxes of product I have at least one complete set of the $M$ coupons.  My attempt has been to take the probability of a coupon not being in a box, use that to determine the probability of that coupon not being in any of the $K$ boxes, and then... I get flummoxed, and don't think this is the correct approach.  I searched the site for coupon collector problems, there are a couple that deal with similar situations (multiple in a box), but with the box having coupons selected with replacement, so duplication in a box is possible.  Right now I'm using a CAS to get probability of sums of hypergeometric samples having all bins covered to check my ideas, but that's utterly impractical for other than tiny cases.   Is this not as trivial as I think it is, or is there a direct way to calculate this? Why is the p-value written with a supremum? I noticed that there is a definition of the pvalue in my textbook is defined says the following:    I have no idea why it is written with a supremum. I've spent hours pondering this, does anyone have enough of a background to help me with this? Thank you! Why does the image not appear? Is there such a thing as a deposit-only bank account? My employer wants me to give my routing-numbers, social-security numbers, and basically everything else required to take money out of my account, to several third-party direct-deposit websites (one for weekly paychecks, one for mileage reimbursements, etc.).  I am not comfortable giving my identity information away to all these places.  I'd like to give them access to an account which they can only deposit into, never withdraw (either a separate account, or, even better, a deposit-only alias to my real account).  Does such a thing exist?    [Edit] I'm not worried about the companies so much as I am worried about bad guys who inevitably hack those companies' databases, or get hired to work there.  This type of account would also be handy for giving read-only access to sites like mint.com or quicken.com, easing my mind about their hackers/unscrupulous employees. I have equations inside an environment which has a larger left-margin than the main text (analogous to an enumerate/itemize environment, implemented with the changepage package's adjustwidth environment). Just as equations in enumerate/itemize behave, the equations are centered with respect to the entire text, rather than just the width of the container environment. I want the latter behavior.  I'm trying to accomplish this by wrapping all display-math in minipages. Namely, I'm modifying the mathdisplay environment in amsmath.sty as follows:  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother   This is almost working, but there are some issues with spacing which I don't understand how to fix. Here's how the the normal \[ ... \] and numbered \begin{equation} ... \end{equation} look with the above modification:      My main confusion is why the numbered version is behaving so differently from the unnumbered. But all in all I want to fix this so that the spacing above and below is even as it usually is. Any help is appreciated, thanks.  Edit: Here's a compilable example:  \documentclass{amsart}  \usepackage{lipsum} \usepackage{calc} \usepackage{changepage}  \makeatletter \let\oldmd\mathdisplay \def\mathdisplay#1{%   \newline   \begin{minipage}{\textwidth-\@totalleftmargin}%     \oldmd{#1}% } \let\oldendmd\endmathdisplay \def\endmathdisplay#1{%   \oldendmd{#1}%   \end{minipage} } \makeatother  \setlength{\parindent}{0pt}  \begin{document}  \lipsum[1]  \begin{adjustwidth}{20pt}{} \lipsum[2] \[ x \mapsto \hom(-,x) \]  \lipsum[3] \begin{equation}   y \mapsto \hom(y,-) \end{equation} \lipsum[4] \end{adjustwidth}  \lipsum[5]  \end{document} Which application does the vi command open? When you type vi in the terminal, the following output is shown  ~                             VIM - Vi IMproved                                 ~                                                                              ~                               version 7.3.547                                  ~                           by Bram Moolenaar et al.                             ~           Modified by pkg-vim-maintainers@lists.alioth.debian.org              ~                 Vim is open source and freely distributable                    ~                                                                                ~                        Help poor children in Uganda!                                                                                So according to this, vi must be launching VIm. But when you type  vim it gives  aditya@aditya-desktop:~$ vim The program 'vim' can be found in the following packages:  * vim  * vim-gnome  * vim-tiny  * vim-athena  * vim-gtk  * vim-nox Try: sudo apt-get install &lt;selected package&gt;   This shows that vim is not installed. Notably man vi and man vim launch the same man pages.  So what does the vi command actually launch? I am using Google Spreadsheets to create a matrix (time/activity) as a daily schedule for staff to sign into.  Is there a formula to calculate the number of cells in a column that are shaded (or not shaded) a certain color?  For example: 20 of the cells are gray and 31 are not gray (shaded any other color) and instead of manually counting them, it calculates this at the bottom of reach column. Calculate the limit of two interrelated sequences? I'm given two sequences:  $$a_{n+1}=\frac{1+a_n+a_nb_n}{b_n},b_{n+1}=\frac{1+b_n+a_nb_n}{a_n}$$  as well as an initial condition $a_1=1$, $b_1=2$, and am told to find: $\displaystyle \lim_{n\to\infty}{a_n}$.  Given that I'm not even sure how to approach this problem, I tried anyway. I substituted $b_{n-1}$ for $b_n$ to begin the search for a pattern. This eventually reduced to:  $$a_{n+1}=\frac{a_{n-1}(a_n+1)+a_n(1+b_{n-1}+a_{n-1}b_{n-1})}{1+b_{n-1}+a_{n-1}b_{n-1}}$$  Seeing no pattern, I did the same once more:  $$a_{n+1}=\frac{a_{n-2}a_{n-1}(a_n+1)+a_n\left(a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})\right)}{a_{n-2}+(a_{n-1}+1)(1+b_{n-2}+a_{n-2}b_{n-2})}$$  While this equation is atrocious, it actually reveals somewhat of a pattern. I can sort of see one emerging - though I'm unsure how I would actually express that. My goal here is generally to find a closed form for the $a_n$ equation, then take the limit of it.  How should I approach this problem? I'm totally lost as is. Any pointers would be very much appreciated!  Edit:  While there is a way to prove that $\displaystyle\lim_{n\to\infty}{a_n}=5$ using $\displaystyle f(x)=\frac{1}{x-1}$, I'm still looking for a way to find the absolute form of the limit, $\displaystyle\frac{1+2a+ab}{b-a}$. What does the size of the standard deviation mean? According to  (my emphasis),     In statistics, the standard deviation ... is a measure that is used to quantify the amount of variation or dispersion of a set of data values. A standard deviation close to 0 indicates that the data points tend to be very close to the mean (also called the expected value) of the set, while a high standard deviation indicates that the data points are spread out over a wider range of values.   The purpose of the standard deviation (SD), then, is to tell us how varied or uniform (SD → 0) the data is.  So, given a certain SD, how varied is the data? What does the size of the standard deviation mean?  Please explain the meaning of the SD by interpreting an SD = 1 (M = 0).  If you cannot interpret the size (quantity) of this SD, what other information would you need to be able to interpret it, and how would you interpret it, given that information? Please provide an example.  If, on the other hand, the quantity of the SD cannot be qualified in this manner, my argument is that it is essentially meaningless. If you disagree, please explain the meaning of the SD.  &nbsp;    The following are earlier versions to give context to the answers. Unfortunately these didn't really convey what I wanted, and my attempt to ask it elsewhere was closed. (I don't need these versions answered now):  First revision:  What does the size of the standard deviation mean?  For example, if I want to study human body size and I find that adult human body size has a standard deviation of 2 cm, I would probably infer that adult human body size is very uniform, while a 2 cm standard deviation in the size of mice would mean that mice differ surprisingly much in body size.  Obviously the meaning of the standard deviation is its relation to the mean, and a standard deviation around a tenth of the mean is unremarkable (e.g. for IQ: SD = 0.15 * M).  But what is considered "small" and what is "large", when it comes to the relation between standard deviation and mean? Are there guidelines similar to the ones that Cohen gives for correlations (a correlation of 0.5 is large, 0.3 is moderate, and 0.1 is small)?    Original question:  We always calculate and report means and standard deviations. But what does the size of the variance actually mean?  For example, assume we are observing which seat people take in an empty room. If we observe that the majority of people sit close to the window with little variance, we can assume this to mean that people generally prefer siting near the window and getting a view or enough light is the main motivating factor in choosing a seat. If on the other hand we observe that while the largest proportion sit close to the window there is a large variance with other seats taken often also (e.g. many sit close to the door, others sit close to the water dispenser or the newspapers), we might assume that while many people prefer to sit close to the window, there seem to be more factors than light or view that influence choice of seating and differing preferences in different people.  At what values can we say that the behavior we have observed is very varied (different people like to sit in different places)? And when can we infer that behavior is mostly uniform (everyone likes to sit at the window) and the little variation our data shows is mostly a result of random effects or confounding variables (dirt on one chair, the sun having moved and more shade in the back, etc.)?  Are there guidelines for assessing the magnitude of variance in data, similar to Cohen's guidelines for interpreting effect size (a correlation of 0.5 is large, 0.3 is moderate, and 0.1 is small)?  For example, if 90% (or only 30%) of observations fall within one standard deviation from the mean, is that uncommon or completely unremarkable? elementary row operation change the eigenvalue of a matrix Exclude a view from master layout? I have a basic doubt about the associativity of the cartesian product. Well, first wikipedia says that the cartesian product isn't associative, and there's a good argument for it: if $x\in E$, $y\in F$ and $z \in G$ the identity $((x,y), z)=(x,(y,z))$ would imply that $(x,y) =x$ and $(y,z) = z$ so that $((x,y),z)=(x,y,z)$ would mean nothing.  That's fine, I like this argument. However, in his book Calculus on Manifolds, Spivak says that the cartesian product is associative. He says: if $A \subset \mathbb{R}^m$, $B\subset \mathbb{R}^n$ and $C \subset \mathbb{R}^p$ then $(A\times B)\times C = A \times (B \times C)$, and both of these are denoted simply by $A \times B \times C$.  Well, this confuses me because Spivak is always very rigorous, so that he wouldn't state something that's not true in such way. Is Spivak or Wikipedia right ? Or Spivak's statement only works for subsets of euclidean spaces ?  Thanks in advance and sorry if this question is too basic. InDesign CS5 tables: Can I automatically fit rows or columns to the size of content? You know how Excel has the function "Autofit," where you select a whole row or a whole column and it resizes the entire thing to the height or depth of the largest content item? I want to do that in an InDesign table, but with one click. (I know I can drag the column out until the overflow box goes away, but I want to know if there's some automated function I'm overlooking.) Does this automatic function exist anywhere? Can I just change straightforward wheel axles to QR skewers?