installing package from a local .tar.gz file on Linux
How do I install an R package from source?
Question  Let $X_n\geq 0$ be independent for $n\geq 1$. The following are equivalent.  $\sum_{n=1}^\infty X_n&lt;\infty$ a.s. $\sum_{n=1}^\infty[P(X_n&gt;1)+E(X_nI(X_n\leq 1)]&lt;\infty$ $\sum_{n=1}^\infty E(X_n/(1+X_n))&lt;\infty$   My attempt I was able to prove $(1)$ implies $(2)$ and $(2)$ implies $(3)$ but not $(3)$ implies $(1)$. For $(1)$ implies $(2)$, observe that by Borel-Cantelli $\sum_{n=1}^\infty P(X_n&gt;1)&lt;\infty$, else $X_n&gt;1$ infinitely often w.p.1 so that $(1)$ is violated. To see that $\sum_{n=1}^\infty E(X_nI(X_n\leq 1)]&lt;\infty$, apply Kolmogorov three-series theorem (I think). For $(2)$ implies $(3)$ we can write that $$ \begin{align} \frac{X_n}{1+X_n}&amp; =\frac{X_n}{1+X_n}I(X_n\leq 1)+\frac{X_n}{1+X_n}I(X_n&gt;1)\\ &amp;\leq X_nI(X_n\leq 1)+ I(X_n&gt;1). \end{align} $$ Now take the expectation of both sides and sum on $n$ using $(2)$ to conclude $(3)$. For the last implication $(3)$ implies $(1)$, I tried to use Kolmogorov three series theorem. To this end put $Y_n=X_nI(X_n\leq 1)$. First note that $\sum_{n=1}^\infty P(X_n&gt;1)&lt;\infty$ since $$ P(X_n&gt;1)\leq P\left(\frac{X_n}{1+X_n}&gt;\frac{1}{2}\right)\leq 2E\frac{X_n}{1+X_n} $$ by Markov's inequality. But I am unable to show that $\sum EY_n&lt;\infty$ and $\sum\text{Var}(Y_n)&lt;\infty$. Any help is appreciated. Python module for converting PDF to text Is there any python module to convert PDF files into text? I tried  found in Activestate which uses pypdf but the text generated had no space between and was of no use. Use mathematical induction to prove $ (2n)!\geq 2^n(n!)^2$ for $n \in \mathbb{N}$ Show that $d_2$ defined by $d_2(x,y)=\frac{|x-y|}{1+|x-y|}$ is a metric I am pretty sure that this is such a stupid, stupid question, but how do you prove that $d_2(x,y)={|x-y|\over {1+|x-y|}}$ satisfying the third condition to be a metric, which is the triangle inequality.   I know that I should really be able to do this, but I just can't, I keep seeing a contradiction. Please help me. What diode modifiers are used in practice to model LEDs with SPICE (Berkeley v.3f5)?  are available to me:  #       Name    Parameter                    Units      Default Example  Area 1       IS      Saturation current             A         1e-14   1e-14    * 2       RS      Ohmic resistance               Ω         0       10       * 3       N       Emission coefficient           -         1       1.0 4       TT      Transit-time                   s         0       0.1ns 5       CJO     Zero-bias junction capacitance F         0       2pF      * 6       VJ      Junction potential             V         1       0.6 7       M       Grading coefficient            -         0.5     0.5 8       EG      Activation energy              eV        1.11    1.11 Si                                                                  0.69 Sbd                                                                  0.67 Ge 9       XTI     Saturation-current temperature exponent  3.0     3.0 jn                                                                  2.0 Sbd 10      KF      Flicker noise coefficient      -         0 11    AF      Flicker noise exponent         -         1 12    FC      Coeff. for for.-bias dep. cap. formula   0.5 13    BV      Reverse breakdown voltage      V         ∞       40.0 14    IBV     Current at breakdown voltage   A         1.0e-3 15    TNOM    Parameter measurement temp.    °C        27      50         The dc characteristics of the diode are determined by the parameters IS and N. An ohmic resistance, RS, is included. Charge storage effects are modeled by a transit time, TT, and a nonlinear depletion layer capacitance which is determined by the parameters CJO, VJ, and M. The temperature dependence of the saturation current is defined by the parameters EG, the energy and XTI, the saturation current temperature exponent. The nominal temperature at which these parameters were measured is TNOM, which defaults to the circuit-wide value specified on the .OPTIONS control line. Reverse breakdown is modeled by an exponential increase in the reverse diode current and is determined by the parameters BV and IBV (both of which are positive numbers).   For example, using this basic, cheap red:      I don't care much about high-frequency characteristics -- just would like to be able to match it's IV-curve within its operating specs (-10uA/-5V leakage to +100mA/+2.2'ishV forward): Random Sample vs. As Large a Sample as Possible? I'm struggling to differentiate scenarios where you would use random sampling vs. getting as large a sample as possible. For instance, one thing I am trying to test is the notion that being in a "home" arena boosts player performance.  I have collected individual football game data for every game over the past 10 years. I have over 34000 observations of players performance during this time span. Would it have been more prudent for me to take a random sample of say, 1000 players over the past 10 years?  I just don't understand why, in the above scenario, I'd take a random sample of 1000 when I can just take all of the players performances from the past 10 years. How to enter the Default Keyring password via the command line? Is there a way to enter the default keyring password using the command line?   For instance:  You have a remote setup of Ubuntu 10.10 thats set to auto login. You don't want to remove  the keyring password.  All right the system boots up and logs in automatically, then asks for the keyring password now at this point you can create ssh connections but you can't remote desktop.   What can you do to enter the keyring password at this point?  Also, to better clarify, this is from a remote connection using the command line. Does payment in goods count as "income" for tax purposes? Can someone help me elucidate the definition of "income" from a tax perspective? More specifically, if Joe is paid for his work in avocados instead of dollars, then would Joe be exempt from paying any income tax for the year? Or would the value of avocados earned for the year be translated into dollars which would then be considered Joe's annual income? If so, what guidelines would one use to make this translation? (Make the assumption that Joe does not sell the avocados (for dollars) at a later date and either eats them or trades them for other real property)  What if he was paid in gold instead of avocados? Spoiler warning!  During the first escape attempt in Portal 2 (when GLaDOS is still in charge) she opens a door for you which you can choose to go through instead of following Wheatley (the blue-eyed ball). What happens if you go there? Windows 8 Pro clean install - everything slow; hard drive at constantly at 100% Yesterday, I have downloaded and installed Windows 8 Professional, after downloading it (legally) and burning it to a DVD, on my 3-year-old  (Intel Core Duo 2x2.4&nbsp;GHz, 4&nbsp;GB RAM,  hard disk drive).   The installation failed two or three times, each time differently (error codes, for example 0xc000021a, with an infinite boot loop), but finally I completely formatted the hard drive and installed. Seemingly, everything was OK.  However, after booting successfully, the OS is extremely slow. When I open the task manager, it shows that the HDD is at 100% - however, no application or background process or Windows process can be made responsible. I searched the Internet and found that Windows might try to "index" the hard drive, but I did't find a process that isn't also on my second computer, which still uses the Release Preview (restarting every two hours). Also, the startup is empty, and HD Tune and HDD Health show that the drive health is OK, even though I don't know how reliable these two programs are.  I looked for diagnose software from Toshiba, but they only offer tools for "Fujitsu branded Toshiba devices"; I tried it out, and it did not work on my hard drive.  Does this sound like a hard drive failure? The laptop is 3.5-years-old, has been carried around sometimes roughly and was used (and on) most of the time. However, it would have failed exactly the night before installing Windows&nbsp;8 Profesional, which seems - unlikely.  If this is a software error - then what did I do wrong if this occurs from the moment of installation (even the personalization at the end of installation took half an hour)? How can I fix this? We add negative numbers and zero to natural sequence to make it closed under subtraction, the same thing happens with division (rational numbers) and root of -1 (complex numbers).  Why this trick isn't performed with division by zero? Class imbalance in Supervised Machine Learning I need to use an alias in the WHERE clause, but It keeps telling me that its an unknown column. Is there any way to get around this issue? I need to select records that have a rating higher than x. Rating is calculated as the following alias:  sum(reviews.rev_rating)/count(reviews.rev_id) as avg_rating Exterior power "commutes" with direct sum I know that for vector spaces $V, W$ over a field $K$, we have the following identity :  $$ \bigoplus_{k=0}^n \left[ \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \right] \simeq \Lambda^n(V \oplus W) $$ which holds in a canonical way : for $0 \le k \le n$, the maps  $$ \Lambda^k(V) \times \Lambda^{n-k}(W) \to \Lambda^n(V \oplus W), \\ (v_1 \wedge\cdots \wedge v_k,w_{k+1} \wedge \cdots \wedge w_n) \mapsto (v_1 \wedge \cdots \wedge v_k) \wedge (w_{k+1} \wedge \cdots \wedge w_n) $$ factors through the tensor product's universal properties, which gives us a map $\varphi_k : \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \to \Lambda^n(V \oplus W)$, and since the category of $K$-modules has biproducts, we get a canonical map  $$ \varphi = \bigoplus_{k=0}^n \varphi_k : \bigoplus_{k=0}^n \left[ \Lambda^k(V) \otimes_K \Lambda^{n-k}(W) \right] \longrightarrow \Lambda^n(V \oplus W) $$  What if I replace $K$ by a (commutative ring with $1$) ring $A$? Does this map have a kernel? I know it is surjective (it suffices to "look at it", i.e generators of the codomain are obviously all hit by $\varphi$). I don't know if it helps, but I am working in integral domains. In the field case, this is obvious if $V$ and $W$ are finitely generated, since one can use dimension arguments. I wouldn't mind if the above identity held only in the finitely generated case either. If it worked in general it would be cool though.   Note that when trying to compute the inverse map with the universal property, there seems to be a problem... my guess would have been $$ (v_1 + w_1,\cdots,v_n + w_n) \mapsto \bigoplus_{k=0}^n (v_1 \wedge \cdots \wedge v_k) \otimes (w_{k+1} \wedge \cdots \wedge w_n) $$ and this map is obviously $A$-multilinear, but there is a problem with the alternating property ; I get some terms left. I'm guessing this is the wrong map... if there is one. How does wizard & cleric spell preparation and casting work? In 3.X wizards had spellbooks, while clerics had their entire spell list, but they both memorized/prepared spells every day from those lists, and had a certain number of slots for preparing spells in.  Now in 5e preparing spells and spell slots aren't the same thing. What's going on here? How does their spellcasting work now? I'm a bit of a force.com IDE newbie - still learning. I'm trying to migrate a simple custom object (no fields) from one sandbox to another and I'm running into this error:  # Deploy Results:    File Name:    package.xml    Full Name:  package.xml    Action:  NO ACTION    Result:  FAILED    Problem: Cannot deploy InstalledPackage in Package Manifest with any other types!   Any help would be greatly appreciated.  Thanks! Pointwise convergent and total variation I'm preparing for a test for real analysis and I came across this problem in Royden's book:  Let $\{f_n\}$ be a sequence of real valued functions on $[a,b]$ that converges pointwisely on $[a,b]$ to the real valued function $f$. Show that $TV(f) \leq \liminf  ~TV(f_n)?$  This looks quite similar in form to Fatou's Lemma to me, but can't find any way to establish TV with integration, can anybody please help?  (TV is short for total variation) How can I watch Amazon Prime videos using Firefox on Ubuntu 16.04? How can I watch Amazon Prime videos using Firefox on Ubuntu 16.04? Currently Firefox version is 48.0. When I attempt to watch a video, I get the following Digital Rights Error message:  Your web browser is missing a digital rights component. In your web browser’s address bar, type about:addons, press Enter, and then on the left, click Plugins. For the Widevine Content Decryption Module, select Always Activate, and then refresh the video’s page and try watching the video. If the video doesn’t play, go back to Plugins, click the gear icon at the top of the page, and then click Check for Updates. When the plugins have updated, refresh the video’s page, and then try watching the video.  I didn't find Widevine Content Decryption Module. I searched for a solution, but it didn't work... One solution I found was to sudo apt-get install flashplugin-installer and then do the following: sudo apt-add-repository ppa:flexiondotorg/hal-flash sudo apt-get update &amp;&amp; sudo apt-get install libhal1-flash  However, it didn't work and I still got the same Digital Rights Error message. I am able to watch Amazon Prime videos using Google Chrome, but not with Firefox. I want to know if it's possible on Firefox on Ubuntu 16.04. I have an HP laptop with with a Core-i5 450m processor and an ATI Radeon 5650 1GB graphics card. When I played crysis warhead on my system its temprature went up to 82° c. Is it safe to play games up to this temperature level? Guides on how to install drivers for a Brother all-in-one network printer are either for older devices or are rather complicated as they often involve editing or copying system files in my root directory.  Is there a newer, more convenient way to install the drivers needed?