This question is directed more towards the hobbyist developer rather than professional game developers.  Quite frequently while developing a game I'll get bored staring at the same exact game scene after days or weeks of work (while new features only slowly creep in) that I find myself abandoning projects and starting new ones, never really finishing what I've started.    How do you prevent yourself from getting bored with a hobby or side project?  What tips/tricks/techniques do you use to keep yourself motivated to actually finish a project?
How can I successfully finish a hobby game project in my free time?  How do I motivate myself to keep it up and drive right through to the finish without losing interest or motivation along the way?
Say I have two independent random variables $X \sim N(u_1, \sigma_1)$ and $Y \sim N(u_2, \sigma_2)$. I want to get the conditional distribution of X given whether X is bigger than Y or not.  $P(X|X&lt;Y)$ = ... and  $P(X|X&gt;Y)$ = ...  I am thinking solving this in this way:  \begin{align} P(X|X&lt;Y) &amp;= \frac{P(Y&gt;X|X)P(X)}{P(Y&gt;X)} \\ &amp;= \frac{(1-\Phi(\frac{x-\mu_2}{\sigma_2}))N(\mu_1,\sigma_1)}{\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})}\\ P(X|X&gt;Y) &amp;= \frac{P(Y&lt;X|X)P(X)}{P(Y&lt;X)} \\ &amp;= \frac{\Phi(\frac{x-\mu_2}{\sigma_2})N(\mu_1,\sigma_1)}{1-\Phi(\frac{\mu_2-\mu_1}{\sqrt{\sigma_2^2+\sigma_1^2}})} \end{align}  My questions are:   (1) Whether above solution is correct  (2) How to get the mean and sd for $P(X|X&lt;Y)$ and $P(X|X&gt;Y)$ if they are still normal? Integral representation of Euler's constant Prove that : $$ \gamma=-\int_0^{1}\ln \ln \left ( \frac{1}{x} \right) \ \mathrm{d}x.$$  where $\gamma$ is Euler's constant ($\gamma \approx 0.57721$).    This integral was mentioned in  as in  , but the solutions I've got uses corollaries from . Can you give me a simple solution (not using much advanced theorems) or at least some hints. What is Skynet's ultimate goal after defeating the resistance? Can the JVM recover from an OutOfMemoryError without a restart What is the difference between an indeterminate and variable? From Wikipedia-     In mathematics, and particularly in formal algebra, an indeterminate is a symbol that is treated as a variable, but does not stand for anything else but itself and is used as a placeholder in objects such as polynomials and formal power series.   So, how it is different from variable which is also used as a placeholder? What is the use of the indeterminate? Retrieving date in sql server, CURRENT_TIMESTAMP vs GetDate() Using SQL Server - which is the fastest or best practice method to use for date retrieval? Is there a difference? Suppose we have a set  $S=\{a,b\}.$ Obviously, the total number of binary operations on $S$ is the number of all the pairs such that $$*(a,b)=a \, \text{or}  \, b,$$ which gives  $ 2 \cdot 2 \cdot 2 \cdot 2=2^4$ possible ones. Is there a way to find which of these $16$ binary operations are associative without writing all the operation matrices and checking it by hand? Why are continuous functions the "right" morphisms between topological spaces? I can't understand how the "cryptographic functions" are to be selected RSA + OAEP which are used in OAEP. How to choose these "cryptographic functions"(G and H)? Theme Image Style for image located in module directory I've finished the game, got all the items except one. This is the one to the right of the green shark fin. What and where is it? How to add readable text to a light and dark image? I'm trying to add text to a photo of a city but the colors in the background make it difficult to read light and dark text. I've tried several light and dark colors but they all looked overpowered by the colors in the image. What colors could I use or what can I do to the text to make it show but also make it so you can still see the background?  Here is the image I'm trying to use: How to install the latest Arduino IDE? 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? Setting ArcGIS Desktop license to lower level for testing whether Python script still runs? I have a Python script that will need to be given to a client.   We are currently evaluating what license level the client will need in order to run the script for their software acquisition purposes.   We all have ArcGIS 10.1 Advanced license in our company.   I checked all the tools and extensions used in the script against the web help and found that they should work on the Standard license level.   Is there a way I can test the script against the Standard license level, when we have no Standard license level in or company (only the higher Advanced level)? Why does pressing a transform hotkey not display the axes on the selected object? I open Blender 2.80 (official release, not a beta or RC) and get the new scene with the usual 3 objects present (camera, light and cube). I select the cube, press 't' for the tools menu and click on the Move tool. The usual 3 axis glyph appears at the cube's origin as expected. But if I use the hotkey 'g' to activate the move transform instead of selecting the tool from the menu with the mouse this glyph does not appear. The exact same problem exists if I use the a hotkey for rotate or scale as well. Why? Is there some clickable checkbox setting hidden somewhere that could have disabled this? I have a skyscraper building but I only want the glass in the texture to be glossy.  How would I accomplish this?    Ok, I have done a test and here are the results.  Here is the original:   here is an adjusted image The continuity of $f(x,y) = \frac {\sin (xy)} {\sqrt {x^2 + y^2}}$ at $(0,0)$ I got a function:       $f(x,y) = \frac {\sin (xy)}  {\sqrt {x^2 + y^2}}$ if $(x,y) \not =  (0,0)$, otherwise $f(x,y) = 0$,   and I should look at its continuity in $(0,0)$   I tried the sandwich theorem but got slightly stuck unfortunately  $ 0 \le \left|\frac {\sin (xy)}  {\sqrt {x^2 + y^2}}\right| \le 1$   I was thinking that $\sin (xy)$ is a restricted function, but not sure what to with $\sqrt {x^2 + y^2}$ if $x,y$ are too small so I think my idea doesn't work. Then it would look like:  $ 0 \le \left| {\sin (xy)} \right| \le \sqrt {x^2 + y^2} = 0$  Any other idea please? If H is a subgroup of a group G and K is a normal subgroup of G the show that K is a normal subgroup of HK. Note K is a normal subgroup of HK  I thought I could just prove K is a subset of HK and vice versa so as to prove it a normal subgroup but then how to do this I have no idea because I keep getting hk element again while trying to do so.  I just tried to implement the steps to find HK is a subgroup of G. Is it unreasonable to assign a MySQL database to each user on my site? I'm creating a user-based website. For each user, I'll need a few MySQL tables to store different types of information (that is, userInfo, quotesSubmitted, and ratesSubmitted).  Is it a better idea to:  a) Create one database for the site (that is, "mySite") and then hundreds or thousands of tables inside this (that is, "userInfo_bob", "quotessubmitted_bob", "userInfo_shelly", and"quotesSubmitted_shelly")  or  b) Create hundreds or thousands of databases (that is, "Bob", "Shelly", etc.) and only a couple tables per database (that is, Inside of "Bob": userInfo, quotesSubmitted, ratesSubmitted, etc.)  Should I use one database, and many tables in that database, or many databases and few tables per database?    Edit:  The problem is that I need to keep track of who has rated what.  That means if a user has rated 300 quotes, I need to be able to know exactly which quotes the user has rated.  Maybe I should do this?  One table for quotes. One table to list users. One table to document ALL ratings that have been made (that is, Three columns: User, Quote, rating).  That seems reasonable. Is there any problem with that?