How to calculate the probability that one random variable is larger than another random variable?
$P(X<Y)$ where X and Y are exponential with means $2$ and $1$
Make locking posts more granular Multiple regression or partial correlation coefficient? And relations between the two I don't even know if this question makes sense, but what is the difference between multiple regression and partial correlation (apart from the obvious differences between correlation and regression, which is not what I am aiming at)?  I want to figure out the following: I have two independent variables ($x_1$, $x_2$) and one dependent variable ($y$). Now individually the independent variables are not correlated with the dependent variable. But for a given $x_1$ $y$ decreases when $x_2$ decreases. So do I analyze that by means of multiple regression or partial correlation?  edit to hopefully improve my question: I am trying to understand the difference between multiple regression and partial correlation. So, when $y$ decreases for a given $x_1$ when $x_2$ decreases, is that due to the combined effect of $x_1$ and $x_2$ on $y$ (multiple regression) or is it due to removing the effect of $x_1$ (partial correlation)? I have several std::vector, all of the same length. I want to sort one of these vectors, and apply the same transformation to all of the other vectors.  Is there a neat way of doing this? (preferably using the STL or Boost)?  Some of the vectors hold ints and some of them std::strings.  Pseudo code:  std::vector&lt;int&gt; Index = { 3, 1, 2 }; std::vector&lt;std::string&gt; Values = { "Third", "First", "Second" };  Transformation = sort(Index); Index is now { 1, 2, 3};  ... magic happens as Transformation is applied to Values ... Values are now { "First", "Second", "Third" }; VMware Linux Server -- how can you tell if you are a vm or real hardware? An interesting question.  I have logged into a Linux (most likely SuSE) host.  Is there some way that I can tell programmatically that I am a VM host or not?    Also assume that the vmtools are not installed. Charging Li-ion batteries in parallel I wanted some opinion on my set up here, just to make sure I got the basics right.  I have a Li-ion battery charging circuit based on the MCP73113. This is designed to be a single-cell battery charger.   The battery itself (3.7V, 650mAh) comes with its own PCB with Schottky diode and current regulators as protection. EDIT: Not a Schottky diode. Current limiter and a Protection IC.  By design, they work together just fine.  I have more batteries from the same manufacturer and wanted to make higher capacity packs by putting two cells in parallel. The two cells come with their own PCB, but I only kept one of them, as I soldered their leads together. It seems to work and they are charged and discharged just like regular batteries (3.7V, now 1300 mAh).  However, not all the packs I made work smoothly and I get a failure rate of 2 in every 10 packs. They all start out normally, but occasionally when the batteries are not charged for some time, or are used up, they tend to not work anymore. So far, in only 1 pack I found the voltage to be different (both now below 2V, aka dead).  I assume my method is not the right approach to ensure 100% success rate, so I was wondering how can this be solved. All the controllers I looked into was designed for multiple cells in series, not parallel. Am I fundamentally missing something here? When can we find holomorphic bijections between annuli? How to install Ubuntu on a Mac and keep OSX? Could anyone provide a concise step by step instruction on how to install Ubuntu 12.04 on a Mac OS X Lion?  I have read that Ubuntu corrupts the EFI file so I would like to hear from those who have successfully done it. Prove Borel Measurable Set A with the following property has measure 0. This question is exercise 4.10 of Richard F. Bass's Real Analysis for Graduate Students, 2nd edition.  Let $\epsilon \in (0,1)$, let $m$ be Lebesgue measure, and suppose $A$ is Borel Measurable subset of $\mathbb R$. Prove that if $$ m(A\cap I)\leq (1-\epsilon)m(I)$$  for every interval $I$, then $m(A)=0$.  Collection of my thoughts  1. Try to prove by contradiction, suppose $m(A)=a&gt;0$ Borel Measurable Set satisfies the condition given. A property of any Borel Measurable Set on $\mathbb R$ is $A$ contains a closed set $F$ and is contained in open set $O$, and the measure of $F$ and $O$ can be arbitrarily close to $a$. 2. Obviously $A$ contains no interval, but it does not lead to contradiction, because we can find an example of $m(A)&gt;0$ that contains no interval(fat Cantor Set(remove middle 1/4 each time) has measure $1/2$ and contains no interval).  2'. For fat Cantor Set $C$ and given $\epsilon&gt;0$ how could we construct an interval I satisfies $m(C \cap I)&gt;(1-\epsilon)m(I) ?$   Maybe try to write Borel measurable set as countable union/intersection of intervals.   I'm stucked here and will appreciate any help, some examples/special case will be great too. Use a specific forwarded key from SSH-agent? Let's say I have a key for Github, along with other keys. I've added lots of keys to my ssh agent (ssh-add -L returns lots of lines) at my home computer A. In my .ssh/config I have set up which key to use with which host, so e.g.  ssh -T -vvv git@github.com 2&gt;&amp;1 | grep Offering   gives  debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.github   Only one key is offered, as expected. But then ssh-ing to some host B with ForwardAgent yes and repeating the same command, I get  debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.linode2 debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.helium debug1: Offering RSA public key: /Users/doxna/.ssh/id_rsa.github   meaning it tries all my keys. This is problematic since only a limited number of keys can be tried before servers return Too many authentication failures. So I tried editing .ssh/config on host B to include  Host github.com   IdentityFile /Users/doxna/.ssh/id_rsa.github   IdentitiesOnly yes   but then I get no key offerings, but rather  debug2: key: /Users/doxna/.ssh/id_rsa.github ((nil))   which I guess means that the key was not found(?) And after all, the key is located at my home computer A, not host B, so the question is how to refer to it at host B? Hope I managed to explain the question. Show that antipodal points remain antipodal under any isometry of $S^2$ "The antipodal map of $S^2$ is the isometry $\bar m$ sending each point $P$ to its opposite point $-P$" (from textbook)  Show that antipodal points remain antipodal under any isometry of $S^2$. In other words, for each isometry f of $S^2$, if $P$ and $P'$ are antipodal, then so are $f(P)$ and $f(P')$  I am unsure how I can define the $P$ and $P'$ so that they are opposites of each other in the antipodal map, and am I supposed to apply the traditional isometries (translation, reflection and rotation) to the points? I don't understand this problem. How do you minimise hand washing between every step to keep tools clean? Say you cooking beef steak:  You have to unwrap the beef from its packaging, lay it down, get blood on your hands, wash hands, sprinkle salt, wash hands, grind pepper, rub the seasoning into the beef, wash hands, grab the tongs etc..  Is it normal to wash hands after every step or is there a trick to avoid getting all the tools dirty?  If you watch TV, they don't ever wash as much as I do. Normal subgroups of infinite symmetric group I recently took a course on group theory, which mentioned that the following proposition is equivalent to the continuum hypothesis: "The infinite symmetric group (i.e. the group of permutations on the set $\mathbb{N}$) has exactly 4 normal subgroups." Does anyone have any references or explanation for this? 'find' utility does not output all files when using wildcards How can I overwrite/print over the current line in Windows command line? On Unix, I can either use \r (carriage return) or \b (backspace) to overwrite the current line (print over text already visible) in the shell.  Can I achieve the same effect in a Windows command line from a Python script?  I tried the curses module but it doesn't seem to be available on Windows. Why is "high" pronounced "hiy" but is not spelled that way? How many sequences of $n$ tosses of a coin that do not contain two consecutive heads have tails as the first toss? If you toss a coin $n$ times, there are $2^n$ possible sequences of heads and tails. Let $E_n$ be the set of sequences which do NOT contain two consecutive heads and $e_n$, the number of sequences in $E_n$.  Thus $E_3$ $=$ $\{$ $TTT$, $TTH$, $THT$, $HTT$, $HTH$ $\}$ and $e_3$ $=$ $3$.  How many elements of $E_n$ have $T$ as the first toss?  Please can anyone help me out here? Fan is always on, CPU usage is rather low and can't find the fan or thermal_zone proc files I have an Asus N76VB notebook with Ubuntu 14.04 and TLP for power managment. However, the fan is always on. It's not really loud, but it's annoying. My CPU usage is around 1-2%. It's clocked at 1.20 GHz.  I've added acpi=force to my boot parameters but it doesn't change anything.  /proc/acpi/fan: No such file or directory /proc/acpi/thermal_zone: No such file or directory   I've loaded all Asus ACPI modules.  lsmod | grep asus:  asus_nb_wmi            16990  0  asus_wmi               24191  1 asus_nb_wmi sparse_keymap          13948  1 asus_wmi video                  19476  2 i915,asus_wmi wmi                    19177  2 mxm_wmi,asus_wmi   Somehow, it can read the temperatures.  sensors:  acpitz-virtual-0 Adapter: Virtual device temp1:        +43.0°C  (crit = +108.0°C)  coretemp-isa-0000 Adapter: ISA adapter Physical id 0:  +44.0°C  (high = +87.0°C, crit = +105.0°C) Core 0:         +44.0°C  (high = +87.0°C, crit = +105.0°C) Core 1:         +42.0°C  (high = +87.0°C, crit = +105.0°C) Core 2:         +39.0°C  (high = +87.0°C, crit = +105.0°C) Core 3:         +39.0°C  (high = +87.0°C, crit = +105.0°C)  asus-isa-0000 Adapter: ISA adapter temp1:        +43.0°C     I really hope someone knows how to solve this. Almost all information I could find was about saving power to create less heat.    I got Intel and NVIDIA (GeForce 740M) graphics but I'm almost anytime on Intel.  $ sudo lshw -c display   *-display                       description: VGA compatible controller        product: 3rd Gen Core processor Graphics Controller        vendor: Intel Corporation        physical id: 2        bus info: pci@0000:00:02.0        version: 09        width: 64 bits        clock: 33MHz        capabilities: msi pm vga_controller bus_master cap_list rom        configuration: driver=i915 latency=0        resources: irq:43 memory:f7400000-f77fffff memory:d0000000-dfffffff ioport:f000(size=64)     fwts fan: Override back button to act like home button Is it OK to require users to have a third party login account? For a web app I'm developing I was dreading having to   Require users to create yet another account / password to keep in mind. Handle retrieval of lost passwords etc.   What many sites (like this one for instance) has started offering is to use a third party account to create an account.   What I wonder is whether it would be considered OK to require having third party account, i.e. Can I create a user-specific hosts file to complement /etc/hosts? Is it possible to add a list of hosts that are only specific to a certain user? Perhaps a user-specific hosts file?  This mechanism should also complement the entries in the /etc/hosts file.