Consider the following function:  $Y(t) = X_1 \exp{(-X_2 t)}$  where the parameters $X_1, X_2$ are random variables and $t$ is the time.  How to find the analytical expression of the probability density function of the function $Y(t)$?
If x and y are uncorrelated normal variates, x*exp(y) will have a symmetric unimodal distribution with positive excess kurtosis. Has this distribution been named and studied?
I'm running a few VMs, and suddenly I noticed my CPU fan was spinning louder than usual. I tracked it down to Windows 8 doing some "automatic maintenance":      How can I turn this completely off? I found a way to set the time, but not a way to turn it off completely. Crick’s Central Dogma — Counter Cases Why does Li+ ion move to cathode in Li-ion battery? How do I disable usb storage? I'm using Ubuntu 12.04 and I want to block usb storage on it. What is the correct way to do this? For linear regression, we can check the diagnostic plots (residuals plots, Normal QQ plots, etc) to check if the assumptions of linear regression are violated.  For logistic regression, I am having trouble finding resources that explain how to diagnose the logistic regression model fit. Digging up some course notes for GLM, it simply states that checking the residuals is not helpful for performing diagnosis for a logistic regression fit.  Looking around the internet, there also seems to be various "diagnosis" procedures, such as checking the model deviance and performing chi-squared tests, but other sources state that this is inappropriate, and that you should perform a Hosmer-Lemeshow goodness of fit test. Then I find other sources that state that this test may be highly dependent on the actual groupings and cut-off values (may not be reliable).  So how should one diagnose the logistic regression fit? If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$ If $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$,then prove that $\sin y=\frac{\sin x(3+\sin^2 x)}{(1+3\sin^2 x)}$    $\tan(\frac{\pi}{4}+\frac{y}{2})=\tan^3(\frac{\pi}{4}+\frac{x}{2})$ $\frac{1+\tan\frac{y}{2}}{1-\tan\frac{y}{2}}=(\frac{1+\tan\frac{x}{2}}{1-\tan\frac{x}{2}})^3$ Applying componendo and dividendo rule on both sides, $\tan\frac{y}{2}=\frac{\tan\frac{x}{2}(3+\tan^2\frac{x}{2})}{(1+3\tan^2\frac{x}{2})}$ I am stuck here. Is there an GUI Designer for python? Is there a GUI IDE for programming python just like java has netbeans?  I wanted one where we could drag &amp; drop test boxes &amp; labels just as we do in swing components using netbeans or eclipse.  Or is there an add-on present in either netbeans or eclipse itself? "He didn't know where New Jersey was" I know the past tense carries the past tense in every dependent clause, but referring specifically to places or to things that are eternal, like the Earth, seems a bit weird and therefore we sometimes (I believe incorrectly) say     He didn't know that New Jersey was actually on the East Coast.   Because it still is. Or     He thought the Earth was round.   So is it square now?  Logically speaking, would you consider the use of past tense here a bit confusing in a day-to-day speech in these examples? Would you instinctively opt for using the present tense? Google Chrome (Windows) not displaying text/encoding correctly on certain websites I experience a problem similar to    Here's a screenshot on the website     I've tried:   Removing fonts I have installed Setting the encoding to Western, UTF-8, Greek, Automatic Changing the fonts used in Google Chrome Removing Google Chrome, including all application data/user profiles Running CCleaner Reinstalling Google Chrome, twice Installing Chromium (fonts display fine in Chromium) Turning off Windows ClearType Changing Windows/Chrome languages from English (Australia) to US, UK Restarting Windows several times after making changes   All of which did not work. I do not connect over VPN/proxy.   Can anyone give me any tips?  Windows 7 x64 Ultimate Can I partition a HDD for playing Xbox 360 games? I am planning to buy an xbox 360 console. my budget permits me acess to only the 4 GB one which needs extra space for many games' install. I have an external HDD of size 40GB. My question is can I divide it into partitions such thet I can use one for gaming on xbox and the other for data storage. How should one maintain and update a MiKTeX installation? Every once in a while after updating MiKTeX, the installation gets into an inconsistent state. This might be a problem with the packages (an example is described in ), but sometimes packages are split or renamed. The cases I remember are when  and when miktex-etex-base-2,9 was renamed to miktex-etex-base-2.9 (if I recall correctly; I am sure it was either that or something very similar). In each case the MiKTeX Update process suggested to remove the "old" packages but it didn't give the user any hints about him having to manually add the respective replacement packages back in the package manager to get one's MiKTeX installation back into a usable state.  What are best practices for keeping MiKTeX up to date? Note that I'm not asking about installing new packages or fonts in general; there are other questions covering this area.   In which order should one execute the Update process and the Synchronization of the repository? , it is recommended to check the MiKTeX homepage before updating. What else should one do? When and in which order (and why) should one execute the "Refresh FNDB" and "Update Formats" processes within the MiKTeX Options menu? What else can happen? Other advice? How can I use $variable in a shell brace expansion of a sequence? I want to use $var in a shell brace expansion with a range, in bash. Simply putting {$var1..$var2} doesn't work, so I went "lateral"...   The following works, but it's a bit kludgey.    # remove the split files echo rm foo.{$ext0..$extN} rm-segments &gt; rm-segments source rm-segments   Is there a more "normal" way? Should reputation from SO carry over to Meta? Proof of sandwich/squeeze theorem for series. Why did the TIE fighter in The Force Awakens have life support? Number of genes required to sustain life Are there estimates of the minimum number of genes required to sustain life?   In what I mean by life here, I don't include viruses. Make flash drive bootable with MULTIPLE Windows Installers I have seen many ways to make a USB an installer for about any Windows OS. But how can I (using grub or something like that) make it bootable to all editions on Windows XP and 7?   I have tried Googling it and researching, I've even tried to do it, But I dont understand much about GRUB or linux at all.  Please keep in mind that I am not very good with linux, so please use as many details as possible. Question about Conditional Expectation I've watched the Vampire Knight anime. I really like the story so far but find it frustrating that the anime doesn't finish off the story. I'm trying to figure out if it is worth reading the manga.  Does the manga contain more story than the anime? Does it finish the story off? Why do we need a Stack Overflow in Portuguese? I have noticed there is a Stack Overflow in language differs from English which is global and mostly used by programmers.  I think there is no need for a site in other languages. Otherwise we will end up with 127 StackOverflow sites. I am afraid that we will lose the amount of people sharing data.