Please can someone explain the steps for deriving the probability density function of median for Normal Distribution
If I calculate the median of a sufficiently large number of observations drawn from the same distribution, does the central limit theorem state that the distribution of medians will approximate a normal distribution? My understanding is that this is true with the means of a large number of samples, but is it also true with medians?  If not, what is the underlying distribution of sample medians?
Tight bound for $T(n) = T(n^{1/2}) + 1$ I am getting this message every time I do something like starting or stopping a service.  perl: warning: Setting locale failed.    perl: warning: Please check that your locale settings:            LANGUAGE = "en_US:en",            LC_ALL = (unset),            LC_MESSAGES = "en_US.UTF-8",            LANG = "en_US.UTF-8"        are supported and installed on your system.    perl: warning: Falling back to the standard locale ("C").    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory    (Reading database ... 21173 files and directories currently installed.)   Removing bind9 ...    * Stopping domain name service... bind9                                        [ OK ] Processing triggers for man-db ...    locale: Cannot set LC_CTYPE to default locale: No such file or directory    locale: Cannot set LC_MESSAGES to default locale: No such file or directory    locale: Cannot set LC_ALL to default locale: No such file or directory      How do I fix this error ? When to use "click" and "click on" How can I publish my game (*.aab file) on google play? Types of polynomial functions. Quadratic, cubic, quartic, quintic, ...,? I would very much like to have a complete list of the types of polynomial functions. I know that theres:  Quadratic :                      (AX^2 + BX + C) Cubic     :               (AX^3 + BX^2 + CX + D) Quartic   :        (AX^4 + BX^3 + CX^2 + DX + E) Quintic   : (AX^5 + BX^4 + CX^3 + DX^2 + EX + F)   What are the names of polynomial functions to the further powers? Sexstic? Septic? Octic? I'm not sure, so if someone could enlighten me, then that would be great. Please provide a list that goes at least to the seventh power, but it would be nice if you could go further. Thanks. Writing C# debug output to .txt file Is drawing multiple cards an atomic action? Is drawing multiple cards an atomic action, or do effects triggered by drawing a card trigger for each card drawn instead?  Consider , which reads:     Whenever a player draws a card, Spiteful Visions deals 1 damage to that player.   If a player were to be compelled to draw more than one card, would that player be dealt the damage all at once, or one at a time? For example, how many times would  need to be activated to prevent all damage?  Furthermore, if there exist additional effects that are triggered by damage dealt in this way, are such effects resolved together atomically or is each resultant effect resolved individually?    How about tutors, or other cards not using the word 'draw', eg:      If you would draw a card, look at the top three cards of your library instead. Put one of those cards into your hand and the rest on the bottom of your library in any order. Partition a set into subsets of size $k$ How to show that $L^p$ spaces are nested? Suppose $1&lt;p_1&lt;p_2&lt;\infty$, then show $L^{p_1}[a,b] \supset L^{p_2}[a,b]$.  I was able to show $\|f\|_{p_1} \le \|f\|_{p_2} (b-a)^{1/p_1 - 1/p_2}$ but I'm not sure how to proceed from here. bash if -a vs -e option Both about -a and -e options in  is said:  -a file     True if file exists. -e file     True if file exists.    Trying to get what the difference is I ran the following script:  resin_dir=/Test/Resin_wheleph/Results  if [ -e ${resin_dir} ] ; then     echo "-e "; fi  if [ ! -e ${resin_dir} ] ; then     echo "! -e"; fi  if [ -a ${resin_dir} ] ; then     echo "-a"; fi  if [ ! -a ${resin_dir} ] ; then     echo "! -a"; fi   /Test/Resin_wheleph/Results exists and is a directory. And this is what I get:  -e -a ! -a   which seems to be a little strange (notice -a and  ! -a). But when I use double brackets (e. g. if [[ -e ${resin_dir} ]]) in the similar script it gives reasonable output:  -e -a   So:    What is a difference between -a and -e options? Why -a produces a strange result when used inside single brackets? Proof of $\int_0^\infty \left(\frac{\sin x}{x}\right)^2 \mathrm dx=\frac{\pi}{2}.$ How do I get the size of a java.sql.ResultSet? Shouldn't this be a pretty straightforward operation? However, I see there's neither a size() nor length() method. Key Presses in Python Remove HTML tags from a String xticks steps using Pgfplots / dateplot Supersymmetry in Quantum Field Theory I have an idea of supersymmetry in quantum mechanics, can you suggest a book on "supersymmetry in quantum field theory", which has sufficient mathematical rigour like "Peskin and Schroeder" How do I identify SMD components? (or how do I identify any component) How do I identify the markings on an SMT component and match it up with a part number so I can be a good designer and actually look at a datasheet (and read the whole thing)? Or identify a part to replace an unknown part on a PCB? I am trying to write an if statement to test whether there are any files matching a certain pattern. If there is a text file in a directory it should run a given script.  My code currently:  if [ -f /*.txt ]; then ./script fi   Please give some ideas; I only want to run the script if there is a .txt in the directory. Should I be worried that yum update suddenly wants to update well over 100 packages on my CentOS 6 system? I have seen some examples about using "in" with time expressions. They give some examples as shown below:     I will leave for vacation in a month. (Exactly one month from now I   will go on vacation.)      We’ll be there in an hour.  (Exactly one hour will go by and then we   will arrive.)   But these comments confused me. Then I looked the usage of "in" up in a dictionary and it says about usage of "in" with time expressions :"before or at the end of a particular period". I think the comments and the definition in the dictionary contradict each other?    I have examples of mine:     1- Dinner will be ready in ten minutes. (Maybe dinner will be   ready at the 5th minute? or 8th. Does it strictly mean dinner will be   ready at the end of the ten minutes?)      2- My letter arrived in two days. ( Does that mean it took   exactly two days to arrive? or Could it be just one day because he/she   doesnt remember the exact time?)      3- Imagine you are on the first day of a month and your friend says:   I will be going outside the country in this month. (Does that mean he/she could go tomorrow or ten days later or at the end of the   month?)      4- He can run a mile in 5 minutes. ( Does that mean he has to   spent entire 5 minutes to run a mile? Could it be 4 or 4.5 minutes?)