If $X_1,...,X_N$ are independent and identically distributed exponential random variables, what can be said about the distribution of $\text{min}(X_1,...,X_N)$ when $N$ is random and modelled as a Poisson random variable?
If $X_1, ..., X_n$ are independent identically-distributed random variables, what can be said about the distribution of $\min(X_1, ..., X_n)$ in general?
How do I find out which version and derivative of Ubuntu is right for my hardware in terms of minimal system requirements? For a given hardware configuration, how do I find out if Ubuntu will run on it? What considerations should I take into account when choosing an Ubuntu version and  such as:    with a lighter desktop than the usual Gnome and Unity  with the even lighter LXDE desktop   Obviously Ubuntu does not run on some processor architectures. So how do I go about choosing the right version and derivate. How can I find out the minmal system requirements? Hoping someone can give me some thoughts on what might be going on here so I can be a bit more informed when I call a plumber.  Situation is, we got our water heater replaced a few years back and ever since this has been an issue. It's more noticeable when it's cold outside it seems, but still seems to be a year round problem. Whenever we  use hot water, we basically run out of it within minutes. In order to get an acceptable amount of hot water (enough to take a 10 minute shower), we literally have to prime the water first. By that I mean I have to turn on the hot water, let it run for a couple of minutes, then turn it off and wait 20 minutes. Then when we go to use the hot water again we'll get hot water for a respectable amount of time. Now I am fairly ignorant to all this, but it seems a 71 gallon hot water heater should be capable of holding enough water to not need to be primed like this. I should be able to take a 30 minute shower, let alone 10 without running out. My shower this morning was decently warm for maybe 2 minutes before it was just warm-ish.   So if anyone can give me some ideas on what might be going on I would appreciate it. We've just put up with this for some years assuming perhaps it was some eco friendly thing. Like the system doesn't maintain much hot water in the tank so it's not always running and only heats water up when you start to use it? I hope that isn't the case though and even so, I should be able to get more hot water out of it. Any help?  UPDATE Sorry everyone, I meant to tell you all that the water heater was gas. The pilot light is lit. I don't recall the specific model though I can look that up if people think it will help. I have actually turned up the thermostat on it above the default and when the water heater is putting out hot water, it can be very hot. Too hot. But again, that requires us to prime it before we get any decent amount of hot water out.  UPDATE 2 Looked it up, I believe this is the model info if that helps anyone: State Select: High Output. Model number: GS675XRRS 300 How to show the number of domains the disk is split into is $1+ C_n^2 + C_n^4$? Assuming there are n points on a circle, then there are $C_n^2$ chords. If any three chords don't intersect in circle. How to show the circle will be divided into $1+ C_n^2 + C_n^4$ domains?  Picture below is a example of 5 points on circle. GUI does not start Initially, the computer was showing the error as mentioned in   question. Fixing it resulted in the above error.  Please take look at the last line   Started GNOME display manager... and deal with any system changes..p link was shut down.....     One more thing before all this problem I have edited xorg.conf file to use  as suggested on .  I don't know if that's the reason but I thought it is important to share. How to run a command that requires sudo at login My OpenID provider is shutting down; how do I change my Stack Exchange login? why does OSX add extra '._' when I tar a directory? I'd just like to know why if I "tar -czf" a file/directory, osx adds a:  ._  for each file? I see these when I untar in linux. Or when I work with the uncompressed project in eclipse as it doesn't like them at all. I use 10.7.5. Sarrus Rule with LaTeX "invalid EFI file path" while booting Windows I just got my new working notebook with Windows 8 pre-installed. After installing Ubuntu 12.10 the grub menu says that there is an "invalid EFI file path" and it won't boot Windows. Ubuntu works fine...  Is there anything I can do about this? Install App Image such as beaker browser and pin it to dock (favorites) in Ubuntu 20.04? After I read that companions don't drain the fusion core of a Power Armor when wearing it, I decided to try giving my armor to Nick so I'll always have it close by if I need it.  But I was wondering if there are any other drawbacks to that. For example, does the Armor get damaged or destroyed when the companion is under fire? How do I show that $\sum_{cyc} \frac {a^6}{b^2 + c^2} \ge \frac {abc(a + b + c)}2?$ Let $a, b, c$ be positive real numbers, show that  $$\frac {a^6}{b^2 + c^2} + \frac {b^6}{c^2 + a^2} + \frac {c^6}{a^2 + b^2} \ge \frac {abc(a + b + c)}2.$$  I think this is likely to turn out to be proved by Hölder, but I can't see how. Any hints will be appreciated. Can I run OSX applications? How to delete contacts from the Windows 8 People app? I never really bothered to keep my Hotmail contact information up to date, so now that I connected it to Windows 8, suddenly I see all this outdated contact information or people I've long stopped talking to.    I don't see any buttons or options where I can click to delete someone.  So how do I clean up my Windows 8 People app and remove these contacts? I just signed up, a day or two ago, and I've received a notification that there's something in my inbox.  Unfortunately, my email client isn't able to show me a link to my Inbox, or the message, because of the format of the email.  I normally use the email address that I gave when I signed up, just with MailWasher, which is intended to safely preview emails, as plain text, to decide whether or not to open them in a normal HTML email client.  I would be nice if that email contained a link to my inbox, which could be shown in MailWasher.  In order to collect that email in a normal email client, I'd also have to collect or delete all the other emails sent to that address.  I'm not entirely clear what's been done in that email to stop MailWasher seeing the link.  I can see a link to leave feedback, and one to unsubscribe, but not one to check my inbox.  Sure, I can live without one, but those emails would be a lot more useful to me if I could just click a link to go to my Inbox. Can there be two winners at the same time in Catan? Imagine the following setup:    Player A has 6 points, including the Longest Road. Player B has 8 points with an equally long road. Player C has 9 points with a shorter road.    Now what would happen if Player C places a village, breaking Player A's road chain? At that moment Player A would have 4 points, while both Player B and Player C would have 10.   In this case, who would be declared the victor? Is there a way to see that $ \nabla_\mu g_{\nu \rho} = 0 $ without explicit computation, where $\nabla_\mu$ refers to the covariant derivative? In books, it is usually said that this is a consequence of the fact that parallel transport preserves dot product. How ? Is it true that for algebraic sets $V,W$ we have $I(V \times W ) =I(V) + I(W)$? Does it make sense to use a date variable in a regression? I'm not used to using variables in the date format in R. I'm just wondering if it is possible to add a date variable as an explanatory variable in a linear regression model. If it's possible, how can we interpret the coefficient? Is it the effect of one day on the outcome variable?   See my  with an example what I'm trying to do. How to configure preferred network for internet? I am connected to a LAN network and wireless network. Both provide access to internet.  Sometimes when the internet on LAN is not working, the browser simply throws an exception instead of switching to Wireless. (Wireless is on and local peer computers on wireless are connectible).  Apparently it is giving more priority to LAN. How do I increase the priority of Wireless or set it as an automatic fall back?