Delete the contents of a huge directory in CentOS 6.6
How can I delete all files from a directory when it reports "Argument list too long"
MLE of $\theta$ when $X_1,\ldots,X_n $ are i.i.d with $P_\theta(x; \theta)=2x/\theta^2$ for $0\le x \le\theta$ 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? I use the babel package in order to write in greek with font "kerkis".  I want to add code in english ("courier new" font) to my latex document but I get some difficulties.  Can anybody help me, please. Thank you in advance.  \documentclass[12pt]{article} \usepackage[english,greek]{babel} \usepackage[utf8x]{inputenc} \usepackage{graphicx} \usepackage{fancybox} \usepackage{verbatim} \usepackage{courier} \usepackage{kerkis} \usepackage{float} \usepackage{geometry} \usepackage{fancyhdr} \usepackage{titlesec} \usepackage{tocloft} \usepackage{hyperref} \usepackage{afterpage} \usepackage{color}    \usepackage{listings}  \renewcommand{\lstlistingname}{Κώδικας}  \lstset{  %matlab   backgroundcolor=\color{white},     basicstyle=\normalsize,    % COURIER NEW?        commentstyle=\color{green},    % comment style   escapeinside={\%*}{*)},           extendedchars=true,               frame=single,                              keywordstyle=\color{blue},       % keyword style   numbers=left,                     numbersep=5pt,                     numberstyle=\normalsize\color{black},    rulecolor=\color{black},           stepnumber=1,                      stringstyle=\color{magenta},     % string style }   \begin{document}  \selectlanguage{greek} Ελληνικά: \textlatin{this word means greek}  \selectlanguage{english} Now I write in english  \selectlanguage{greek} Ελληνικά  %\selectlanguage{english}???  \begin{lstlisting}[caption = \textlatin{example1.m}] { % Entropy E = 0; for i = 1:J     if p(i) ~= 0         E = E + p(i)*log2(1/p(i));     end end } \end{lstlisting}  \end{document} The height of a string in a gravitational field in 2-dimensions is bounded by $h(x_0)=h(x_l)=0$ (nails in the wall)  and also $\int_0^l ds= l$. ($h(0)=h(l)=0$, if you take $h$ as a function of arc length) .  What shape does it take?  My try so far: minimise potential energy of the whole string,  $$J(x,h, \dot{h})=\int_0^l gh(x) \rho \frac{ds}{l}=\frac{g \rho }{l}\int_0^l h(x) \sqrt{1+\dot{h}^2} dx$$  With the constraint  $$\int_0^l \sqrt{1+\dot{h}^2} dx- l=0$$ If it helps, it's evident that $\dot{h}(\frac{l}{2})=0$.  Generally, this kind of equation is a case of a constrained variational problem, meaning that the integrand in  $$\int_0^l \frac{g \rho }{l}h(x) \sqrt{1+\dot{h}^2} +\lambda(\int_0^l \sqrt{1+\dot{h}^2} dx- l)dx$$  Must satisfy the Euler Lagrange equation. The constraint must also be satisfied.  But, in truth, by this point I am clueless. $\lambda$ is worked through $\nabla J  = \lambda \nabla(\int_0^l \sqrt{1+\dot{h}^2} dx- l)$. I have tried this , but get nonsensical answers.  Is this method the best? If so, in what ways am I going about it wrongly thusfar? What is the historic present tense? I learned that the historical present may be used to create an effect of immediacy in narratives. I have a question about the historic present tense. Why don't we use the progressive tense instead of the simple present tense?   ※My English skill is poor, so my question might sound rude. But I don't mean to offend anyone. I'd be glad if someone could reply to my question. Determine whether a number is prime How do I determine if a number is prime?  I'm writing a program where a user inputs any integer and from that the program determines whether the number is prime, but how do I go about that? In some papers or documents, "linear times series" seems to refer to a time series that can be modeled as a linear AR (auto-regressive) model.   In other places, "linear time series" seems to refer to a time series with a linear trend.   When someone just drops "linear time series" out of the blue without any context, what do they mean usually? Show that conguence $\bmod m\,$ is an equivalence relation Why define an anonymous function and pass it jQuery as the argument? When I use \listoftables and \listoffigures I get in the list long captions that appear next to the tables/figures.  I would like to use short captions for this list which summarize these captions. Is that common to do? If so, what is one way to do it? What does [param: NotNull] mean in C#? Where did object dimensions go in 2.8? This morning I read this sentence (see ):     On July 24th and again on July 29th,   Egyptian police did shoot dead unarmed   African migrants attempting to cross   that border.   Why "did shoot" and not "shot"? How do I remove the space between inline/inline-block elements? CHAOS members have (had?) :     Because they are doing so many edits at once, CHAOS operates in a special mode where editing a title does not bump it to the home page.    I moderate at Writers.SE, and I can attest that this ability would be extremely beneficial to mods as well, and for the same reasons. On beta sites, wide-ranging changes are not infrequent. An established tag might be ruled problematic; a certain class of questions might need cleanup; etc. etc.. When this happens, the ensuing edits flood the front page with old content (frequently the somewhat problematic content the new change has come to address...). Furthermore, since beta sites are much less active than established ones, this flood can drown out recent activity, and then wallow around on the front page for some time.  I propose, then, the implementation of a moderator tool for editing without bumping. The value to beta sites is clear; the danger of abuse, as a mod tool, is nonexistent. How do I find (or exclude) all directories and sub-directories matching a certain pattern (in Linux)? I have a product key for windows 8.1 (Single language edition or not that i can't remember). I have currently windows 10 pro installed.  I am planning to install windows 10 Home so i activate with windows 8.1 key.  So my question is will i be able to activate it if the Product Key is Windows 8.1 Single Language and i install Windows 10 Home(Multiple language edition) or vice versa. What is the progression route in Terraria? On finding polynomials that approximate a function and its derivative (extensions of Stone-Weierstrass?) The Stone-Weierstrass Theorem tells us that we can approximate any continuous $f:\mathbb{R}^n\to\mathbb{R}$ arbitrary well on a compact subset of $\mathbb{R}^n$ by some polynomial. Suppose that $f$ is continuously differentiable, under what conditions can we guarantee we can find a polynomial $p$ such that $p$ approximates arbitrarily well $f$ and the partial derivatives approximate of $p$ arbitrarily well those of $f$ (on a compact subset of $\mathbb{R}^n$)? References are welcome. See below for my (probably naive) approach to the question.    It is straightforward to find conditions if $n=1$: Let $K:=[a,b]\subseteq\mathbb{R}$ and let $K_+$ denote some open cover of $K$. Suppose that $f:K_+\to\mathbb{R}$ is continuously differentiable and let $f'$ denote its derivative. Then, by Weierstrass's approximation Theorem we have that there exists a polynomial $q$ such that   $$||f'(x)-q(x)||\leq \varepsilon$$  for all $x\in K$. Choose some $y\in K$. For any $x\in K$ define  $$p(x):=f(y)+\int_y^xq(t)dt.\quad\quad(*)$$  By the Fundamental Theorem of calculus we have that $p'=q$. So for any $x\in K$  $$||f(x)-p(x)||=\left|\left|\int_y^x (f'(t)-q(t))dt\right|\right|\leq \int_y^x ||f'(t)-q(t)||dt\leq \varepsilon||x-y||\leq \varepsilon (a-b).$$  However, the above argument doesn't work in higher dimensions because the analogue of $(*)$ does not imply that $\nabla p = q$ (since not every vector of polynomials spans a gradient field). Can anyone suggest a way around this? That is, a way to to show that for continuously differentiable $f:\mathbb{R}^n\to\mathbb{R}$ and for any $\varepsilon&gt;0$, we can always find a polynomial $p$ such that   $$||f(x)-p(x)||+||\nabla f(x)-\nabla p(x)||\leq \varepsilon$$  for all $x$ in some compact set $K$? Feel free to add extra conditions on $K$, if it makes life easier. The energy of a moving object is $E = mv^2\;.$ That is it increases with velocity squared.  I walk at say 3 miles per hour, or lets round that down to 1 meter per second for a slow walk. I weigh less than $100~\mathrm{kg}\;,$ but lets just round that up to $100~\mathrm{ kg}$ for convenience (it is just after Christmas).  So when I walk along the pavement, I have $100~\mathrm{kg\; m^2 s^{-2}}$, 100 joules of kinetic energy.  Now I get on a passenger jet, which is cruising at around 500 knots, call that 250 meters per second.  In my seat I have $100\times 250^2 = 6250000$ joules of kinetic energy. But when I walk down the aisle I have $100\times 251^2 = 6300100$ joules of kinetic energy. The difference between these is: 50100 joules.  It feels the same to me, walking down the pavement as walking down the aisle of the plane. I didn't have to make some huge effort to get up to speed on the plane, yet I needed 500 times the energy to do it.  How is this possible, and where did the energy come from? Differentiation operator and eigenvalues Let $V = \{p(x) \in F[x] \ | \ \deg(p(x)) \le n\}$. Let $T : V \to V$ be given by differentiation, in essence $$T(p(x)) = p'(x)$$ It seems to me that the only eigenvalue that can exist is $\lambda =0$, since the given operator lowers the degree of any given polynomial and hence makes it impossible for a constant multiple of a polynomial to be equal to the polynomial's derivative. Is my claim correct?