Intuition behind a conditional probability problem
How to develop intuition for conditional probability?
Using swap space instead of RAM can drastically slow down a PC.  So why, when I have more than enough RAM available, does my Linux system (Arch) use the swap?  Checkout my conky output below:    Also, could this be the cause of speed and system-responsiveness issues I'm having?  Output of free -m :  $ free -m              total       used       free     shared    buffers     cached Mem:          1257       1004        252          0         51        778 -/+ buffers/cache:        174       1082 Swap:          502        144        357 Is there a constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$? Assuming the Axiom of Choice, every vector space has a basis, though it can be troublesome to show one explicitly. Is there any constructive way to exhibit a basis for $\mathbb{R}^\mathbb{N}$, the vector space of real sequences? Generalized Pell equation $x^2-2y^2=49$ On this site I see hundreds if not a thousand questions being asked about issues with a Wireless LAN adapter not being detected/recognized by Ubuntu. Some mainstream adapters appear to be utterly broken in Linux support, while others just require some simple steps to get it to work.  The options to get it to work appear to be infinitely huge and I have no clue where to get started!  What is considered 'best practice'? What order of things to try is most efficient in terms of time, effort and imposes minimal risk to my Ubuntu installation? Please help me save time and guide me what to do, step by step. Are there any guidelines for converting cooking recipes from Regular Ovens to Convection? I was looking to buy a Convection Oven and wanted to know if there are any general differences in baking methods between the two. In a complete metric space with no isolated points, any countable intersection of open dense sets is uncountable? The residue at $\infty$ I am stuck on the following problem :      $\,\,\,\,$*Problem*$\quad$The residue of an entire function at $\infty$ is $0$.      Solution: True. This follows from the definition of the residue at $\infty$ together with the Cauchy-Goursat Theorem. Another way to see this is to take the Taylor expansion for $f$ at $0$ $\displaystyle f(z)=\sum_{n=0}^\infty a_nz^n$ and replace $z$ with $1/z$ to get the Laurent expansion for $f(1/z)$ at $0$: $\displaystyle f(z)=\sum_{n=-\infty}^0a_{-n}z^n.$ Then we have that the residue at $\infty$ is given by the negative coefficient of the $1/z$ term of    $$ \dfrac1{z^2}f\left(\dfrac1z\right)=\sum_{n=-\infty}^{-2}a_{-n-2}z^n, $$   which is clearly $0$.   I am having trouble to understand the last few lines (in italic) in the given solution. Can someone give lucid explanation? Thanks and regards to all. How to Make Multi User Objects Single User? I duplicated a few objects with Alt+D and now I want to apply some modifiers to them, however I can't, because they are multi-user objects.  I tried U > Objects but I still can't apply the modifier.  How to make multi user objects single user? What is the value of $\sum\limits_{i=1}^\infty\dfrac{1}{p_{p_i}}$ where $p_n$ is the nth prime (and so $p_{p_n}$ is the $k$th prime, where $k$ is the $n$th prime) ?  Thus $\frac{1}{3}+\frac{1}{5}+\frac{1}{11}+...=$ ??  How do I efficiently decide if $\sum_{i=1}^\infty\dfrac{1}{p_{p_i}}\gt1$ is true without using a computer ?  I assume this infinite sum is an irrational number. Has this already been proven ? Bounded operator that does not attain its norm What is a bounded operator on a Hilbert space that does not attain its norm? An example in $L^2$ or $l^2$ would be preferred.  All of the simple examples I have looked at (the identity operator, the shift operator) attain their respective norms. Mail vs. mail what is the difference 2.5 GB usable out of 4 GB of ram How to read the content of a file to a string in C? How do I create a dynamic key to be added to a JavaScript object variable What do they do with all the plates and cups in Star Trek? Whenever someone in Star Trek creates food or drink in the replicator it is generated in the bowl, plate, or cup. It seems like after a few months they would have piles of used dishes from replicator food while making more for every meal. What do they do with all the dishes? how to represent geography or zip code in machine learning model or recommender system? I am building a model and I think that geographic location is likely to be very good at predicting my target variable.  I have the zip code of each of my users. I am not entirely sure about the best way to include zip code as a predictor feature in my model though.  Although zip code is a number, it doesn't mean anything if the number goes up or down.   I could binarize all 30,000 zip codes and then include them as features or new columns (e.g., {user_1: {61822: 1, 62118: 0, 62444: 0, etc.}}.  However, this seems like it would add a ton of features to my model.   Any thoughts on the best way to handle this situation? What is the use of the Dot Product of two vectors? Is it possible that galaxies' redshift is caused by something else than the expansion of space? I was thinking that maybe photons loss energy naturally when they travel great distances.  Or maybe the mass of all matter is increasing over time and therefore photons emitted in the past are necessarily less energetic.  Or is the expansion of space backed up by so much other evidences that trying to find another explanation is completely foolish? Rewriting Triple Integral in different order How can I rewrite, say: $$\int^1_0\int^{z^2}_0\int^y_0{f}dxdydz$$ In the orders $dzdxdy$ and $dydzdx$?  Would I have to solve this triple integral all the way or is there a simple way to do this? Subject–verb agreement not clear in "Is two bars OK?" Is the following correct?     Can I get some chocolate for myself? Yes, you can but not much.   Is two bars OK?   Is there any rule to explain the sentence above?  The dialogue's taken from Grammar Textbook Round-Up Level #3.