'I badly need to _' and 'I want to _ so bad'
Can "real" be used as an adverb to describe an adjective?
Assume the standard situation, that is, let $X_1, \ldots , X_n$ be independent and identically distributed with $X_k ∼ P_\theta(x; \theta)$ , where $P_\theta(x; \theta) = 2x/\theta^2$  if $0\le x \le\theta$ and $0$ otherwise. It is required to estimate $\theta$. Show that the maximum likelihood estimator for $\theta$ is $\hat{\theta} = \max{[X_1, \ldots , X_n]}$ and then show that the cumulative distribution function of $\hat{\theta}$ is $F_\theta(z) = z^{2n}/\theta^{2n}$. Here's what i did so far: Maximum Likehood estimator: $L_x(θ) = \prod_{i = 1}^{n} P_θ(x_k)$ Here we have $P_θ(x_1,...,x_n;θ) = P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)$ Likehood = $L_{x,θ}(θ) =P_θ(x_1,θ).P_θ(x_2,θ)...P_θ(x_n,θ)= 2x_1/θ^2. 2x_2/θ^2.. 2x_n/θ^2 = [2^n.\prod_{i = 1}^{n}x_i]/θ^{2n}$ Log-likehood: $\sum_{i = 1}^{n}log(P_θ(x_1,...x_n;θ))= \sum_{i = 1}^{n}log(2x_i/θ^2)$ Is this correct so far? Im still not sure how to get to $\hat{θ} = max{[X_1, . . . , X_n]}$ As for the the cumulative distribution part to show $F_θ(z) = z^{2n}/θ^{2n}$: $F(z) = P(max({x_k})&lt;z) = P(x_1&lt;z).P(x_2&lt;z)..P(x_n&lt;z) = 2x_1/θ^2.2x_2/θ^2...2x_n/θ^n = 2^n.\prod_{i = 1}^{n}x_i/θ^2n$ Not sure if this is correct. Would really appreciate some help. Edit: From the answers below, we can deduce the the estimator is biased. What estimator would be unbiased? How can i find it? "Dummy Output" No sound in Ubuntu 16.04 None of the HDMI output are working, all saying "dummy output", it was working yesterday, but when I use the headphones it became soundless, with or without the headphones.  Thank you already! How to find vendor and model of unknown drivers I reinstalled windows on a new machine and the drivers are not present for the product network card.   When in device manager all I get is the question mark and I am unable to figure out the actual name of the vendor or model of the card. This is making my search to find the correct driver hard.   Anyone know how I to find out more about the hardware that does not have drivers? How can I install Sun/Oracle's proprietary Java JDK 6/7/8 or JRE? Prove that $\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$ Problem  Suppose $f$ is a non-negative integrable function on a measure space $(X,\mathcal{A},\mu).$ Prove that $$\lim_{t\to \infty} t\mu(\{x:f(x)\geq t\})=0$$  Attempt  Let $E_t=\{x:f(x)\geq t\}$ Note that $f\chi_{E_t}\leq f$. Since $f$ is integrable, the Lebesgue dominated convergence theorem tells us that $$\lim_{t\to\infty} \int f\chi_{E_t}\rightarrow \int \lim_{t\to\infty} f\chi_{E_t}=0,$$ since $\lim_{t\to\infty} f\chi_{E_t}=0$ a.e. $\ ^{(1)}$ The result follows from the fact that $$t\mu(E_t)\leq\int f\chi_{E_t}.$$  Question  I am having trouble proving $(1)$. That is, how can I show that $f\chi_{E_t}\rightarrow 0$ a.e? Best practice for Rails App to run a long task in the background? I have a Rails application that unfortunately after a request to a controller, has to do some crunching that takes awhile.  What are the best practices in Rails for providing feedback or progress on a long running task or request?  These controller methods usually last 60+ seconds.    I'm not concerned with the client side... I was planning on having an Ajax request every second or so and displaying a progress indicator.  I'm just not sure on the Rails best practice, do I create an additional controller?  Is there something clever I can do?  I want answers to focus on the server side using Rails only.  Thanks in advance for your help.  Edit:  If it matters, the http request are for PDFs.  I then have Rails in conjunction with Ruport generate these PDFs.  The problem is, these PDFs are very large and contain a lot of data.  Does it still make sense to use a background task?  Let's assume an average PDF takes about one minute to two minutes, will this make my Rails application unresponsive to any other server request during this time?  Edit 2:  Ok, after further investigation, it seems my Rails application is indeed unresponsive to any other HTTP requests after a request comes in for a large PDF.  So, I guess the question now becomes: What is the best threading/background mechanism to use?  It must be stable and maintained.  I'm very surprised Rails doesn't have something like this built in.  Edit 3:  I have read this page: .  I would love to read about various experiences with these tools.  Edit 4:  I'm using Passenger Phusion "modrails", if it matters.  Edit 5:  I'm using Windows Vista 64 bit for my development machine; however, my production machine is Ubuntu 8.04 LTS.  Should I consider switching to Linux for my development machine?  Will the solutions presented work on both? What is the difference between Interest Rate and APY on savings accounts, CDs, etc?  Is there a simple formula to convert the two? Injecting beans into a class outside the Spring managed context I'm an end-user of one of my company's products. It is not very suitable for integration into Spring, however I am able to get a handle on the context and retrieve the required bean by name.  However, I would still like to know if it was possible to inject a bean into this class, even though the class is not managed by Spring itself.  Clarification: The same application which is managing the lifecycle of some class MyClass, is also managing the lifecycle of the Spring context. Spring does not have any knowledge of the instance of MyClass, and I would like to some how provide the instance to the context, but cannot create the instance in the context itself. I'm trying to install pandas. When I do, it's automatically installing to the python installation for v 2.7.   How do I force pandas to install to the python 3.5 installation? I need to do this for displacement mapping, subdivision gives a bad result and makes triangles distinguishable.    Related to:   But I get the error "No other selected object found to use for projection". Regression Proof that the point of averages (x,y) lies on the estimated regression line How do you show that the point of averages (x,y) lies on the estimated regression line? Change logo url link As far as I can tell, it's something like this:  damage reduction = armor / (armor + 100)   Is this accurate? I have a batch file which I use to create an .apk file on my Windows machine. Now I need to be able to create the .apk file in Ubuntu but I don't know how translate my .bat file to a script to be able to run it on Ubuntu.  Below is the batch file which works fine on Windows.  Will you please give me some hints on how I can run it on Ubuntu?  @echo off set PAUSE_ERRORS=0 :user_configuration  :: Path to Flex SDK  set FLEX_SDK=C:\sdk\flex_sdk_4.5.1.21328  :: Path to Android SDK set ANDROID_SDK=C:\sdk\android  :validation if not exist "%FLEX_SDK%\bin" goto flexsdk if not exist "%ANDROID_SDK%\platform-tools" goto androidsdk goto succeed  :validation if not exist "%FLEX_SDK%\bin" goto flexsdk if not exist "%ANDROID_SDK%\platform-tools" goto androidsdk goto succeed  :flexsdk echo. echo ERROR: incorrect path to Flex SDK echo. if %PAUSE_ERRORS%==1 pause exit  :androidsdk echo. echo ERROR: incorrect path to Android SDK in 'bat\SetupSDK.bat' echo.  if %PAUSE_ERRORS%==1 pause exit  :succeed set PATH=%PATH%;%FLEX_SDK%\bin set PATH=%PATH%;%ANDROID_SDK%\platform-tools  :: Android packaging set AND_CERT_NAME="PeymanApp" set AND_CERT_PASS=fd set AND_CERT_FILE=cert\SampleApp.p12 set AND_ICONS=icons/android  set AND_SIGNING_OPTIONS=-storetype pkcs12 -keystore "%AND_CERT_FILE%" -storepass     %AND_CERT_PASS%  :: Application descriptor set APP_XML=application.xml  :: Files to package set APP_DIR=bin set FILE_OR_DIR=-C %APP_DIR% .  :: Your application ID (must match &lt;id&gt; of Application descriptor) set APP_ID=air.com.doitflash.SampleApp  :: Output packages set DIST_PATH=dist set DIST_NAME=PeymanApp  :validation %SystemRoot%\System32\find /C "&lt;id&gt;%APP_ID%&lt;/id&gt;" "%APP_XML%" &gt; NUL if errorlevel 1 goto badid goto end_validation  :badid echo. echo ERROR: Application ID (APP_ID) does NOT match Application descriptor '%APP_XML%'     (id)  echo.  :end_validation  set TARGET= set PLATFORM=android  ::call bat\Packager.bat if "%PLATFORM%"=="android" goto android-config  :android-config set CERT_FILE=%AND_CERT_FILE% set SIGNING_OPTIONS=%AND_SIGNING_OPTIONS% set ICONS=%AND_ICONS% set DIST_EXT=apk set TYPE=apk goto start  :start if not exist "%CERT_FILE%" goto certificate :: Output file set FILE_OR_DIR=%FILE_OR_DIR% -C "%ICONS%" . if not exist "%DIST_PATH%" md "%DIST_PATH%" set OUTPUT=%DIST_PATH%\%DIST_NAME%%TARGET%.%DIST_EXT% :: Package  echo true echo. call adt -package -target %TYPE%%TARGET% %OPTIONS% %SIGNING_OPTIONS% "%OUTPUT%"     "%APP_XML%" %FILE_OR_DIR% -extdir lib/ echo. if errorlevel 1 goto failed goto end  :certificate echo Certificate not found: %CERT_FILE% echo.  if %PAUSE_ERRORS%==1 pause exit  :failed echo APK setup creation FAILED.  if %PAUSE_ERRORS%==1 pause exit  :end How do I get a tourist visa (or a tourist card) for Cuba?  I live in the Netherlands, but I'm not a Dutch citizen, I have an Italian passport. Zero visitors? What happened to site analytics about a week ago? When is assembly faster than C? One of the stated reasons for knowing assembler is that, on occasion, it can be employed to write code that will be more performant than writing that code in a higher-level language, C in particular.  However, I've also heard it stated many times that although that's not entirely false, the cases where assembler can actually be used to generate more performant code are both extremely rare and require expert knowledge of and experience with assembly.    This question doesn't even get into the fact that assembler instructions will be machine-specific and non-portable, or any of the other aspects of assembler.  There are plenty of good reasons for knowing assembly besides this one, of course, but this is meant to be a specific question soliciting examples and data, not an extended discourse on assembler versus higher-level languages.  Can anyone provide some specific examples of cases where assembly will be faster than well-written C code using a modern compiler, and can you support that claim with profiling evidence?  I am pretty confident these cases exist, but I really want to know exactly how esoteric these cases are, since it seems to be a point of some contention. How does a zener diode and a resistor regulate voltage? If $\lim_{x\to\infty}(f(x)+f'(x))=L$ show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$ Let $f:(0,\infty) \to R$ be differentiable. Suppose that $\lim_{x\to\infty}(f(x)+f'(x))=L$. Show that $\lim_{x\to\infty} f(x) = L$ and $\lim_{x\to\infty} f'(x) = 0$. (Hint: Write $f(x) = e^xf(x)/e^x$ and use l’Hopital’s Rule.)    My working for $\lim_{x\to\infty}f'(x)=0$:  For $\lim_{x\to\infty}f'(x) = 0$, I let $f(x) = e^xf(x)/e^x$ and applied quotient rule which then cancels off $e^{2x}$ and I'm left with $\lim_{x\to\infty}(f(x)+f'(x)-f(x))$. Can I then equate this with $\lim_{x\to\infty} \left(f(x)+f'(x)\right) - \lim_{x\to\infty}f(x)$ which then gives $L-L=0$? Is this step correct? How to plot ROC curves in multiclass classification? In other words, instead of having a two class problem I am dealing with 4 classes and still would like to assess performance using AUC.