Bit copied a disk image using the dd command to a new and bigger disk. How do expand whole LVM?
Ubuntu: Resize the root LVM(2?) partition
Prove $\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$ I've been given a proof that shows the following:  If $f:[a,b]\to \mathbb C$ is a continuous function and $f(t)=u(t)+iv(t)$ then $$\left| \int_a^b f(t) dt \right| \leq \int_a^b \left| f(t) \right| dt$$ The proof begins by letting $\theta$ be the principle argument of the complex number $\int_a^b f(t)dt$ and there is one step in the proof I don't understand; can anyone explain to me why $$\int_a^b e^{-i\theta}f(t) dt=\Re\bigg(\int_a^be^{-i\theta}f(t)dt\bigg)$$  Would this not imply that the imaginary part of the left hand side is equal to $0$? I'm not sure why the LHS and RHS would be equal here. Key to get help about current function Reading InputStream as UTF-8 gdal_translate- why jpg compressed tif is 2 times greater than jpg file? Do you have recommendations for books to self-teach Applied Statistics at the graduate level? I took several statistics courses in college but I found that my education was very theory driven.  I was wondering if any of you had a text in Applied Statistics (at the graduate level) that you recommend or have had good experience with. Prison problem: locking or unlocking every $n$th door for $ n=1,2,3,...$ I have a problem called "The Prison Problem" that I need to explain to my 9-year-old cousin. I would think that he has just started learning about divisors and perfect squares, and as such, I have a proposed solution. Any input from you guys would be welcome, as to what is the best way to go about this.  Problem:  There was a jail with 100 cells in it, all in a long row. The warden was feeling very jolly one night and told his assistant that he wanted to give all the prisoners a wonderful surprise. While they were sleeping, he wanted the assistant to unlock all the cells. This should be done, he told the assistant, by putting the key in each lock, turning it once. The assistant did this, then came back to report that the job was done. Meanwhile, however, the warden has second thoughts. "Maybe I shouldn't let all the prisoners free," he said. "Go back and leave the first cell open, but lock the second one (by putting the key in and turning it once). Then leave the third open, but lock the fourth, and continue in this way for the entire row." The assistant wasn't very surprised at this request as the warden often changed his mind. After finishing this task, the assistant returned, and again the warden had other thoughts. "Here's what I really want you to do," he said. "Go back down the row. Leave the first two cells as they are, and put your key in the third cell and turn it once. Then leave the fourth and fifth cells and turn the key in the sixth. Continue down the row this way." The assistant again did as instructed. Fortunately, the prisoners were still asleep. As a matter of fact, the assistant was getting pretty sleepy, but there was no chance for rest yet. The warden changed his mind again, and the assistant had to go back again and turn the lock in the fourth cell and in every fourth cell down the row. This continued all through the night, next turning the lock in every fifth cell, and then in every sixth, and on and on, until on the last trip, the assistant just had to turn the key in the hundredth cell. When the prisoners finally woke up, which ones could walk out of their cells?  Proposed solution:  Ten cells are left open after this process. Every cell that is a perfect square will remain open (1, 4, 9, 16, 25, 36, 49, 64, 81, and 100). If a number is not a perfect square, then it has an even number of divisors, therefore it will be "toggled" an even number of times and end up where it started (closed). Perfect squares have an odd number of divisors, so they will end up the opposite of where they started (open). Extract substring in Bash Is the matrix diagonalizable for all values of t? The the title is self explanatory, I guess.  Why can two (or more) electric  never cross? Subgroups of $U(n)$ isomorphic to a direct sum of cyclic groups Let $U(n)$ to be the set of all positive integers less then $n$ and relatively prime to $n$. Then $U(n)$ is a group under multiplication modulo $n$.  A. Find integer $n$ such that $U(n)$ contains subgroup isomorphic to $Z_5\oplus Z_5$.  B. Show that there is an $U(n)$ containing a subgroup isomorphic to $Z_3 \oplus  Z_3$, but not isomorphic to $Z_4 \oplus  Z_4$. Why does Maximum Likelihood estimation maximize probability density instead of probability I am trying to understand Maximum likelihood estimation but it looks like I am missing something rather elementary.          suppose we have an iid random sample $X_1, X_2,..., X_n$ for which the probability density function of each $X_i$ is $f(x_i; \theta)$ where $\theta$ is an unknown parameter. Then, the joint probability density function of $X_1, X_2,..., X_n$ is given by:          $f(X_1=x_1,X_2=x_2,\cdots,X_n=x_n)=\prod_{i=1}^{n} f(x_i, \theta)$      In Maximum Likelihood estimation, we try to maximize $f$ as a function of $\theta$.  Question: Why do we maximize probability density instead of probability? In what way does it make sense?  Edit: As explained in the answers, the probability of choosing a finite number of sample points from a continuous probability distribution is zero, so maximizing probability doesn't make sense, but how does maximizing probability density make sense? How to create a folder in HOME Folder with ModelBuilder in ArcGis 10? There are n letters addressed to n eople at different addresses. The n addresses are typed on n envelopes.  A disgruntled secretary shuffles the letters and puts them in the envelopes in random order, one letter per envelope.  Find the probability that at least one letter is put in a correctly addressed envelope. [Hint: use the inclusion-exclusion formula.] What is the probability approximately, for large n ?    My attempt at a solution:  P(all correct) = $\frac{1}{n!}$  P(n-1 correct) = ${n \choose n-1} \frac{1}{n!} = \frac{1}{1!(n-1)!}$  ${n \choose n-1}$ ways of selecting n-1 correct letters.  P(n-2 correct) = ${n \choose n-2} \frac{1}{n!} = \frac{1}{2!(n-2)!}$  ...  P(n-n correct) = ${n \choose n-n} \frac{1}{n!} = \frac{1}{n!(n-n)!} = \frac{1}{n!}$  This all looks ok to me, but I tested this for a case of 4 people, (I think the theoretical value should be $\frac{9}{24}$ but obviously that is not what I got. Can someone correct my logic please? Also, with regards to the hint about inclusion/exclusion - where would that come in?  I read about derangements on Wikipedia but it did not make total sense to me (the derivation).  I would appreciate any advice whatsoever including references to other material. Opposite of "straight talk" What is the opposite for the straight talk idiom? How do I best call the activity when someone makes a very long preamble before he says what he wants? Is this defined by the language? Is there a defined maximum? Is it different in different browsers? $\mathbb{Q}(\sqrt{p},\sqrt[3]{q})= \mathbb{Q}(\sqrt{p}\cdot \sqrt[3]{q})$ ?? Kernel Panic - not syncing: VFS: Unable to mount root fs on unknown-block(0,0) I noticed that, for each research project, there comes a point where I have to consult the literature, and find all the previous research related to the current project.  Unfortunately, I seem to be very inefficient in my approach. I spend a lot of time digging through papers that are really interesting, but only of tangential importance to my current work, just to find the few papers that actually do similar things. (The pile of "cool paper, read when time" just keeps growing.)  Hence, I'm wondering: What is the most time efficient way to get a thorough overview of the literature in a specific niche of a field?    While searching for an answer I came across these questions:   - This question is quite similar and I liked the approach. I debated with myself if this is a duplicate, but I think it is focused more on how to be sure the search was exhaustive, whereas I'm worried about time efficiency. (Also, I'm a bit curious if things have changed since 2012.)   - The answer provides tips on how to identify what literature generally is important in a field, but I am looking for the most cost effective (least time consuming) way to do it in an area, where I know the broad literature, but not the specifics. $|f'(x)| \le g(x)$ implies $|f(b) - f(a)| \le \int_a^b g(x) dx$, without assuming $f'$ to be integrable. Command not found $ (dollar sign) Any command that starts with $ returns  command not found   How can I fix this?  I am  using 16.10 Ubuntu.