Sum of gamma distributions and its mean
Why is the sample distribution the Exponential distribution Gamma distributed?
Why is there an emission of gamma rays? When a spontaneous radioactive reaction happens, there is an emission of gamma rays (in most cases) What causes this emission? How can I make extra money with photography? I have photos in Getty Images, in Shutterstock, Imagekind and I recently added some to RedBubble, but I'm not having the expected results.  Does anyone have some history of success selling photographs or working as a photographer?  Examples of my work are available in .    Also asked by   I am an amateur who sometimes takes pictures of nature or random things. I've been told by several people that my pictures are worth money.  How can I monetize my best shots?  I don't really want to do a lot of work, editing, SEO or whatever. I'm looking for an easy way where I would just upload my pictures somewhere and let it go.  Maybe stock photos? People buying prints? I have no idea how that works...  EDIT: maybe a link to see which type of photography I do can help How to count the number of set bits in a 32-bit integer? Will I still receive OTA updates after rooting my Nexus 5? I just wanna ask that after rooting Nexus 5 will I be receiving OTA updates by Google ? Or I'll have to install a custom ROM ? Show that $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$ Let IG denote Inverse-Gamma distribution   .   If $X\sim IG(\alpha,1)$ and $Y\sim IG(\beta,1)$. Show that   $\frac{X}{X+Y}\sim Beta(\alpha,\beta)$   I tried with jacobian transformation taking $Z=\frac{X}{X+Y}$ and $W=Y$ then $$X=\frac{WZ}{1-Z};Y=W$$  $$\frac{\partial(z,w)}{\partial(x,y)}=\frac{1}{(1-z)^2}$$  $$f_{z,w}(z,w)=f_x(\frac{wz}{1-z})f_y(w)(1-z)^2$$ $$f_{z,w}(z,w)=\frac{1}{\Gamma{(a)}}(\frac{wz}{1-z})^{-\alpha-1}e^{-\frac{(1-z)}{wz}}\frac{1}{\Gamma{(\beta)}}w^{-\beta-1}e^{-\frac{1}{w}}(1-z)^2$$  but I'm stuck, in some place I read that $\frac{X}{X+Y}$ is a type 3 Beta distribution, but I can't show that. In blender cycles render engine, how do I put a movie clip on a plane so it displays the video? I want the video to be on the plane if there is a way. In ubuntu 11.04 there was a workaround using gconf-editor and setting key /apps/gnome_settings_daemon/plugins/xrandr/active to false.  However there is no such key in gconf-manager using ubuntu 11.10 (gnome 3). How does java do modulus calculations with negative numbers? Efficient online linear regression Bounded measurable function and integral with charcteristic function Give a combinatorial proof: $ n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} $ Find a combinatorial argument for the following binomial identity:   $$n(n+1)2^{n-2} = \sum_{k=1}^{n}k^2\binom{n}{k} .$$   Algebraic proofs can be found at  , and a related identity at  . Friend was brainwashed by MLM-/ponzi investment scam. What can I do? Recently a friend of mine invited me to hear about “an interesting chance to simply earn money.” Basically we and other invited people drove to a meeting room where a speaker told us about a growing startup where you could invest money in a field where similar investments had an ROI of apparently 1000 times the investment in 6 years. Afterwards there was coffee and small talk together, during which they also indoctrinated people saying, they should avoid talking to people talking bad about the investment (or saying it is scam) because you can't gain money from them and they just want to destroy your business.  You earn money if you invest money and if you refer friends who invest money up to multiple levels. The more you invest yourself the greater percentage you earn for your referrals.  Since I had already seen other ponzi-/MLM-schemes and I am from the field it is based in, I recognized that there is no real product and it is a ponzi-/MLM-scheme. Later I found its name on the official scam warning list of multiple countries.  From what I understand, my friend has already invested multiple months or years worth of income; and is earning an amount of money through referrals that would mean scamming other people directly or indirectly through referrals for possibly several $100,000's per month to earn an additional bonus. He also wants to use his position as a respected member of multiple local youth groups and other community groups to get their members as referrals or in his words “…to give them the opportunity to also simply earn money.”  I tried to convince him that it is just a ponzi scam with my knowledge in this field but he answered with the indoctrinated speech “You don’t need to know the details if it makes you rich or use it. You also don't know how every detail of a smartphone works?”/“My sponsor already earned $x with this” or “If you don't believe in this, just stop talking about it to me and other people or do you want to ruin me, my business and my investments?.” So basically this means I can either make his investment worthless/let him lose everything (he also quit his job) or let him scam other people and motivate them to scam other people.  At the moment you can only withdraw small amounts of money out of it because the company invented some reason but you will be able to withdraw all of it “soon” (=most likely never).  What is the best way to resolve this situation (best meaning with lowest loss of money for everybody)?  Edit: The founders are known names in Ponzi schemes or convicted for crimes like fraudulent bankruptcy and many of their claims are technically impossible or proven to not exist with very high probability according to sites about ponzi schemes. But of course they say "Every bigger company has their scandals".  You can't trade the bought virtual coins outside the company and the only product you can buy can be bought anywhere else for less than 10% of the price without the logo.  When I met other friends they mentioned that they got invitations for the same meeting. I just stated to them that I already went to one and told them the name of the company (which was not stated on the invitation) and that I will not invest in it because there are official warnings that this is a scam. Why can't Mathematica integrate this? Refer to renamed columns in WHERE clause SELECT name, gdp/population as capita  FROM world w1  WHERE continent = 'Europe'       AND capita &gt;  (     SELECT gdp/population      FROM world      WHERE name = 'United Kingdom' );   How come I can't refer to capita in the WHERE clause? It returns this error:  Unknown column 'capita' in 'where clause'   I can however, run the query if I replace capita with gdp/population.  I don't want to do gdp/population &gt; .... How can I do capita &gt; ...? Or is this not possible? What are the practical applications of the Taylor Series? I started learning about the  in my calculus class, and although I understand the material well enough, I'm not really sure what actual applications there are for the series.  Question: What are the practical applications of the Taylor Series? Whether it's in a mathematical context, or in real world examples. Labelled spanning trees of $K_n-e$ Let $e$ be an edge of $K_n$- the complete graph on $n$ vertices. Prove that the number of labelled spanning trees of $K_n-e$ is $(n-2)n^{n-3}$.  I think the answer lies in using some modified form of Prüfer's sequence but I can't quite nail it. Ubuntu 18.10: visual artifacts (black bar) in dock if extend-height is disabled I am using the default Ubuntu dock with bottom placement and org.gnome.shell.extensions.dash-to-dock extend-height set to false. With Ubuntu 18.10 this produces a noticeable visual glitch, note the black empty spaces at the edges of the dock:    I am getting this both on an upgraded system and on a clean install inside a VM. This was working fine in Ubuntu 18.04. Also happens if the theme is set to something else than Yaru (the default theme in Ubuntu 18.10). Reboot does not help. Dock looks OK if extend-height is enabled.  Any ideas on how to fix this? Is there anyway to sync Outlook's calendar with Google's calendar? I've tried  before but it doesn't work properly. I'm using Windows 7 and Outlook 2010.  The thing is, it's really easy to check my Google Calendar on my phone since I have an Android terminal, but on my computer I prefer just opening Outlook instead of opening a web browser and logging into Gmail. Let $A$ be a diagonalizable matrix and $\lambda$ be an eigenvalue of A. Prove that rank($\lambda I - A$) = rank(($\lambda I - A)^2$). JavaScript + Unicode regexes