I need help to understand the probability derviation of a paper. Please help me. For the following, please only treat $|h_{R,B}|^2$ and $|h_{A,R}|^2$ as random variables (other parameters can be treated as constants). Those two random varibles are i.i.d. such that they are exponential distributed with parameter $E[|h_{R,B}^2|]$ and  $E[|h_{A,R}^2|]$ respectively for $|h_{R,B}|^2$ and $|h_{A,R}|^2$.  In particular, I don't understand what he did after line 74 (the yellowed part).
So assume $Y$ and $X$ are exponentially distributed with parameters $y_1$, and $x_1$ respecitively.  assume c is a constant.  I am having huge trouble to understand the integration of the following expression.  $P(Y&lt;c/u(X))$  $=\int_{t}^{\infty}f_X(x)\int_{0}^{c/u(x)}f_Y(y)dydx +\int_{0}^{t}f_X(x)\int_{c/u(x)}^{\infty}f_Y(y)dydx$  where t is the cross-point that $u(x)$ change sign    here $c/u(x)$ is given by the plot below, t is the point crossing the zero:   Confusion:   I don't understand the second integration of the second term "$\int_{c/u(x)}^{\infty}f_Y(y)dydx$", this isn't right because Y an X only defined for y>0, and x>0. So it's the first quadrant in this plot.
ACPI error when trying to make dual boot with Ubuntu 18.04 and Windows 10 Ralink MT7601U (148f:7601) Wi-Fi adapter installation I am trying to install a Ralink wifi adapter in Ubuntu Desktop 14.04.  The system is not detecting the wifi.   lsusb lists the device as:  Bus 002 Device 004: ID 148f:7601 Ralink Technology, Corp.  I have the rt2800 USB driver listed in "/etc/modules"; Following some instructions on the web, I tried this command:  echo 148F 7601 | sudo tee /sys/bus/usb/drivers/rt2800usb/new_i  lsmod | grep rt2800 returns the following:  rt2800usb              26581  0  rt2x00usb              20041  1 rt2800usb rt2800lib              83150  1 rt2800usb rt2x00lib              48886  3 rt2x00usb,rt2800lib,rt2800usb mac80211              545990  3 rt2x00lib,rt2x00usb,rt2800lib crc_ccitt              12627  1 rt2800lib Can anyone explain to me why I would want to use IList over List in C#?  Related question: A   B   C   D   E   F             I don't even know. It just seemed weird.  Yes, I understand I could just avoid doing something like that. But the problem already exists with a single level.   Consider having 2 images in a post. Both exceed the maximum width of a post. One is nested in a list. Key to this issue is that my original images were much larger. They were automatically resized.  Image    List      I think it looks weird. I'm looking for some way to run a batch file (.bat) without anything visible to the user (no window, no taskbar name, .etc..).  I don't want to use some program to do that, I'm looking for something cleaner. I've found  that uses VBScript, but I don't really like using VBS, either. Why are my sauces splitting? Integrable function whose Fourier transform is not integrable In document class book, and package caption, creating index with makeidx. Index entries for the main text and for footnotes collate properly; but those for captions create their own entries.  Example: for the tag \index{New York!Custom House!\textit{Cartouche}}, text and footnotes collate properly; but used in a caption, a new entry is created at the third level, and is also out-of-alphabetic-sequence. Note: the top level, and first sub are correct; only the second sub is duplicated.  How to get the caption index entries under the same entry? Say you have the infinitely continued fraction: $$x+\cfrac{1}{x^2+\cfrac{1}{x^3+\cfrac{1}{x^4+\ddots}}}$$ When $x=1$, you can see that it's $$1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\ddots}}}$$ which converges upon the golden ratio $\phi = 1.61803398875...$. What if I were to plug in $x=2$? $$2+\cfrac{1}{4+\cfrac{1}{8+\cfrac{1}{16+\ddots}}}$$ Using a caluclator, it seems to converge upon the irrational number: $2.24248109286...$ Is there any way I can represent this irrational number algebraically? I have a set of surround speakers, connected to my iMac through the headphone jack. I use a switch to control what goes to the speaker set (iMac, iPod, or MacBook/aux). So that I don't have to be constantly unplugging and replugging, I leave the audio cable in the iMac's audio port. This means that when I'm listening to something from another source, I can't hear anything from the iMac unless I unplug the cable.  Is there a way to force sound to come out of the internal speakers, even if there's something in the audio out port? PHP Session Security What are some guidelines for maintaining responsible session security with PHP?  There's information all over the web and it's about time it all landed in one place! I am using Google Chrome 48.0 32-bit. Today when I launched Google Chrome, I got this message:    This computer will soon stop receiving Google Chrome updates because this Linux system will no longer be supported   I thought Ubuntu 14.04 is supported for five years, what's exactly happening here?  And on 64-bit Ubuntu, I get an error from Update Manager and apt-get update:  Failed to fetch http://dl.google.com/linux/chrome/deb/dists/stable/Release  Unable to find expected entry 'main/binary-i386/Packages' in Release file (Wrong sources.list entry or malformed file)   Some index files failed to download.   They have been ignored, or old ones used instead. For all square matrices $A$ and $B$ of the same size, it is true that $(A+B)^2 = A^2 + 2AB + B^2$? The below statement is a true/false exercise.  Statement: For all square matrices A and B of the same size, it is true that $(A + B)2 = A^2 + 2AB + B^2$.  My thought process: Since it is not a proof, I figure I can show by example and come to a valid conclusion based on such example.  My work:  Come up with a square matrix A and B let both be a 2 by 2 matrix(rows and cols must be same).  Matrix $A$:  $A = \begin{array}{ccc} 3 &amp; 5 \\ 4 &amp; 6 \\ \end{array} $  Matrix $B$:  $B =  \begin{array}{ccc} 5 &amp; 8 \\ 9 &amp; 4 \\ \end{array} $  $A + B =  \begin{array}{ccc} 8 &amp; 13 \\ 13 &amp; 10 \\ \end{array}$  $(A + B)^2 =  \begin{array}{ccc} 233 &amp; 234 \\ 234 &amp; 264 \\ \end{array}$  $A^2 =  \begin{array}{ccc} 29 &amp; 45 \\ 36 &amp; 56 \\ \end{array}$  $(AB) =  \begin{array}{ccc} 60 &amp; 44 \\ 74 &amp; 56 \\ \end{array}$  $2(AB) =  \begin{array}{ccc} 120 &amp; 88 \\ 234 &amp; 112 \\ \end{array}$  $B^2 =  \begin{array}{ccc} 97 &amp; 72 \\ 81 &amp; 88 \\ \end{array}$  $A^2 + 2AB + B^2 =  \begin{array}{ccc} 246 &amp; 205 \\ 265 &amp; 256 \\ \end{array}$  Based my above work, the answer is false.   Is there another way to approach the problem? It seems like a lot of work needed to be done for a true/false question which raised my suspicion about whether there is a better way to look at the problem. Video produced from images only plays in VLC but no other players How do electrons jump orbitals? My question isn't how they receive the energy to jump, but why.  When someone views an element's emission spectrum, we see a line spectrum which proves that they don't exist outside of their orbitals (else we would see a continuous spectrum).  Electrons can be released in the form of beta decay, thus proving that they are capable of traveling outside of orbitals contrary to the statement my teacher said that they stay within orbitals. Then, to add to the confusion, the older model of rings floating around a nucleus has, from what I can tell, been outdated, which would support this model. My teacher's explanation was that the electrons made a quantum jump of some kind. How do electrons move between orbitals or do we know how they jump, excluding the reason that energy causes them to jump, and why are positrons formed sometimes instead of electrons in Beta decay?  When I'm asking "how do electrons jump" I would like to know how an electron can jump between each orbital such as how it moves and how it knows where to jump since it appears to be a jump where the electron doesn't slow into a orbital position. Specifically how they jump what is this Atomic electron transition, I understand that they jump and that they do this through absorbing and releasing energy but what is this Atomic electron transition other than what is already on the wikipedia article . Can we omit a duplicated preposition? Is on needed a second time in this sentence?        There is a bad effect either on human health or environment.    There is a bad effect either on human health or on environment. "right" vs "correct" Except when we use right to denote direction, what is the difference between these two terms?  Also, which one is the preferred construction between these two     Am I right?   or     Am I correct? What the pointer size in 64 bits computer in C++? "He needn't say" / "He doesn't need to say" When I studied English at school (in Italy, more than 35 years ago), we were taught a rule according to which one should say, e. g., "He needn't (need not) say", but NOT "He doesn't need to say".  If I'm not mistaken, it was explained to us that the rule holds good with the following limitations:  1) only in the negative form: thus, "He needn't say", but "He needs to say", and "Does he need to say?";  2) only in the present tense: thus, "He needn't say", but "He didn't (won't, wouldn't, etc.) need to say";  3) only when an infinitive follows: thus, "He needn't see a doctor", but "He doesn't need a doctor".  But, if I google "doesn't need to", I find 125,000,000 occurrences.  I was wondering: does the rule hold good more for British than for American English?  Also, perhaps it isn't an absolute rule, and both constructions ("He needn't say" and "He doesn't need to say") are possible.  Is the rule at least a good description of the circumstances when we CAN (but needn't necessarily) use this construction?  Thank you very much, for this and the other answers. I have an issue which I could not solve, although I tried and I got some help on R forum.  I am trying to calculate Mahalanobis distances on a data.frame, where I have several hundreds of groups and several hundreds of variables. Whatever I do, I get the system is computationally singular: reciprocal condition number error.   It is clear that it is singular, but is there any way to get rid of it and run Mahalanobis? Should I forget solve this using another approach? If yes, then what else to use?  I have uploaded the data file to my :  It is a tab delimited txt file with no headers.  I was working with the R StatMatch Mahalanobis (also tried stats Mahalanobis) function. I have a deadline for this project (not a homework!), and I could always use this function, so I thought I will be able to keep the calculations short, but now I am lost.  Migrated .