I am referring to this  page 198-9:    I have troubles understanding the case with unequal variance.  In general it :   or on :    Therefore if we assume unequal variance, I would think like this:  $s_{\bar{X}_T-\bar{X}_C}=\sqrt{s^2_T/n_1+s^2_C/n_2}$  Howerver, they give this for the standard error:    I have troubles with deriving these two different formulas.
I encountered such a formula for pooled variance:  $$\frac{(n-1)s_x^2+(m-1)s_y^2}{n+m-2}\left(\frac{1}{n} + \frac{1}{m}\right)$$  Here we have two samples of the following sizes $n$ and $m$. $s_x, s_y$ are the sample variances.  I understand that the first term is a weighted average, but from the second term comes?
Can you stay in Turkey for over 90 days within the 180 day visa period but split over different visits? The Turkish e-visa is valid for a period of 180 days and allows you to stay for a maximum of 90 days. Am I allowed to stay for say 50 days, then another 50 days, over two different visits within the 180 day period?  I'm looking at the e-visa website  and it doesn't seem to be too clear on this. Centre of Lie Algebra $sl_2(\mathbb{F})$ For $L=sl_2(\mathbb{F})$ i.e. matrices with trace zero,  what is the centre i.e. $Z(L)$= {$x\in L : [x,y]=[y,x] \ \forall\ y \in L$}.  I will have to find matrices $A \in L$ such that $AB=BA$ for all $B \in L$. But how to appoach this considering trace is zero here. There is this puzzling thing that is called : paradoxically, warm (35°C) water freezes faster than cold (5°C) water.  As a physisist, I've been asked about it several times already. And I have no definite answer to that, apart from the standard: "there are many things that can influence it".  So, does anyone knows about the status or progress on that effect? Any recent reviews, publications or other references? We were trying to come up with an easy way to generate a rational number in between two existing rational numbers with a fairly low numerator and denominator (the way we were doing this earlier was to find the average of the two rationals, but that results in a denominator of up to $c * d$. Does this inequality hold for all values of $a, b, c, d$? How do I include a custom class file in a module? In Drupal 7 module development, I could include a custom inc, api, or php class file using the  directive in the module.info file or the drupal_load_included() function.   With D8 using PSR, what is the proper way to package up a "plain ole PHP object" and reference it in DefaultController.php? Think something like: $a = new POPO();.  Is just giving the PHP file containing the class a namespace sufficient? How does the controller (or module in general) know to reference or scan for that class? Old TV mini-series with a living brain in a lab Travelling as unmarried couple in Dubai "Lunch" vs. "dinner" vs. "supper" — times and meanings? I've seen cases where a noon-time meal is referred to as dinner, and the evening meal is called supper. There's also lunch around noon followed by dinner in the evening. Is there a particular difference between dinner and supper, or a circumstance where lunch becomes dinner? Evaluating the sum $\Sigma \, \frac{1}{k(k+p)}$ How can I run ssh-add automatically, without a password prompt? I want to communicate between several computers on my network (static Ethernet), through SSH. In order to do that I need to run ssh-add every time I log in on a specific machine, how can I do it so that it's set up once and it doesn't ask me for the passphrase every time I log in or reboot my machine?  I know that there is a way that you should add some lines to the bash_profile file, but I still need to type the password every time I reboot/log in to a specific machine.  if [ -z "$SSH_AUTH_SOCK" ] ; then     eval `ssh-agent -s`     ssh-add fi Imagine your college buddy is now running a multi-billion dollar company, while you're still stuck at the same white-collar day job 5 years after graduation. You chat with him and want to express the idea that you're happy for him and fancy having his lifestyle--something like "I wish I could buy a yacht and cruise around the world like you do; I'm glad you're doing really well!"  Basically, it's the feeling of envy when you take out the resentment from it. Is there a word for it?   (I thought about "admire", but found it too strong and broad) I uninstalled my wine, and installed a higher version of wine by compiling source.  However when I run an exe executable (whose path is in $PATH), it doesn't work as it used to:  $  PDFXCview.exe     run-detectors: unable to find an interpreter for /home/tim/program_files/document/pdfxchange_portable/PDFXCview.exe   I am not sure why I was able to run this executable directly before I uninstalled my old wine and installed the new one. How can I make $  PDFXCview.exe work now?  Note:  $ wine /home/tim/program_files/document/pdfxchange_portable/PDFXCview.exe   will work.   $ wine PDFXCview.exe   wine: cannot find L"C:\\windows\\system32\\PDFXCview.exe"   doesn't work. Note that the path of PDFXCview.exe is still in $PATH  Thanks. sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot be used in production organizations While deploying code in vsCode from sandbox to production I get the below error      sf:INVALID_OPERATION: INVALID_OPERATION: testLevel of NoTestRun cannot   be used in production organizations   As per the error, I need to change the value of testLevel but I am not able to find where and how can I change it to RunLocalTests  Could someone please help me to change the value of testLevel in vsCode I have a Red Hat Enterprise Linux server (7.5 x86_64). I have OpenSSH version 7.4. I was asked to upgrade it to a later version for security reasons: Nessus states that . However the Red Hat software and downloads does not have the latest package RPM.  I found some clues on where to get the latest package for OpenSSH. I found , however, I do not know on how to upgrade it and trust this website. I do not want the SSH and other configuration to be modified by the ugrade.  I did find links but however they are not useful, for example .  I would like to know how to upgrade OpenSSH without using yum. How to efficiently find positions of duplicates? Having trouble indexing and executing a query in O (log n) time.  The query includes an INNER JOIN, an ORDER BY, and an equality operation. If I understand the laws of databases correctly, a query can be indexed and executed in O (log n) time (or thereabouts) if a non-equality operator is not used on more than one column. In this case, I believe the INNER JOIN does count as an equality operator and the non-equality operator would be the ORDER BY portion of the query. This table has upwards of 10,000,000 rows and needs to handle several reads and writes per second.  Using PostgreSQL. This is what the table looks like. As you can see, the column 'Names' is a list property and it is the column that the INNER JOIN goes against:  Age Names                       Date 34  ['carla', 'john', 'sam']    3/13/2011 26  ['json', 'cindy', 'joel']   3/13/2011 72  ['beth', 'amber', 'susie']  3/13/2011 14  ['john', 'jim', 'debie']    3/13/2011   This is the query that we are trying to do:  SELECT * FROM the_table WHERE Age==26 AND Names=='john' ORDER BY Date   My background is from using App Engine's Big Table, so I've used equality operators here to indicate that 'john' should be one of the names in the Names column. This would be an acceptable query in GAE's big table, it would execute in O (log N) time as all Big Table queries are reqyured to do. I am assuming there is a way to do this in PostgreSQL as well since PostgreSQL accepts list data types as columns.  Is this possible to do in PostgreSQL?  If so, how should the index be set up (we can't figure out how to set up an index that takes into account the three properties)? How to update the PATH user environment variable from command-line How can I install a Canon printer or scanner driver? tikz declare function and babel french option Unable to change payment information to NONE in iOS Appstore