Could not run sudo apt-get update
How do I fix the GPG error "NO_PUBKEY"?
Are nested functions a bad thing in gcc ? Traveling Amsterdam-Brussels with KLM ticket on Thalys - When / where does my ticket get stamped? Let $a_n=\sqrt[n]n-1$. Does $\sum_{n=1}^\infty a_n$ converge? How to show a binomial random variable dominates another binomial random variable with a smaller success value? Let $X\sim B(n,p_h)$ and $Y\sim B(n,p_\ell)$ be two random variables following a respective binomial distribution, where $p_h&gt;p_\ell$. I want to show that  $$P(X\ge\alpha)\ge P(Y\ge\alpha),$$ for any $\alpha\in\{0,1,\dots,n\}$. In other words, I want to show  $$P(X\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge P(Y\ge\alpha)=\sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  The statement to be proven is obviously true, but proving it is extremely difficult (at least for me). Can anyone give me some guidance on proving it?  It would be nice if someone can give an algebraic proof too, that is, show that  $$\sum_{i=\alpha}^{n}\binom{n}{i}p_h^i(1-p_h)^{n-i}\ge \sum_{i=\alpha}^{n}\binom{n}{i}p_\ell^i(1-p_\ell)^{n-i}.$$  Thank you very much! I've come across a small issue which occurs when a question has been closed but the question itself or one of its answers are being edited.  Steps to reproduce:   Visit a closed question. (even closed years ago)   In a different tab or browser, edit the question or one of its answers. "an edit has been made to this post; click to load" message will appear above the edited post in the first tab/browser, click it. The .question-status div becomes hidden, which includes the closed notice below a question and, for a duplicate-closed question, the list of duplicates above the question body. This gives the appearance that the question is no longer closed (until you refresh).   Some screenshots:                I know it isn't common/important but it did confuse me when looking at a particularly bad question - I thought it had been reopened.   Is this an intentional feature? If so, what was the thinking behind it?    Another example  Before    After I'm using custom post types, but they don't appear on tag pages along with regular posts and i'd like to include both standard and custom post types on tag or category pages. What would be required before the loop to include all posts? (including custom type). Updated: To add, I found this code , which worked perfectly for the first part: add_filter('pre_get_posts', 'query_post_type'); function query_post_type($query) {   if ( is_category() || is_tag() &amp;&amp; empty( $query-&gt;query_vars['suppress_filters'] ) ) {     $post_type = get_query_var('post_type');     if($post_type)         $post_type = $post_type;     else         $post_type = array('post','cpt'); // replace cpt to your custom post type     $query-&gt;set('post_type',$post_type);     return $query;     } }  Second question still remains though: Is there a way to allow readers to filter by post type? So either of the following would work..  example.com/tag/blue?post_type=custom example.com/tag/blue?post_type=post How do I resolve "WILL_NOT_PERFORM" MS AD reply when trying to change password in scala w/ the unboundid LDAP SDK? How do I do Combinatorics / Counting? If someone could give answers and explain, it would be greatly appreciated. Help required studying for a final.  One hundred tickets, numbered 1,2,3,…,100, are sold to 100 different people for a drawing. Four different prizes are awarded, including a grand prize (a trip to Tahiti).   A) How many ways are there to award the prizes?  B) How many ways are there to award the prizes if the person holding ticket 47 wins the grand prize?  C) How many ways are there to award the prizes if the person holding ticket 47 wins one of the prizes?  D) How many ways are there to award the prizes if the person holding ticket 47 does not win a prize?  E) How many ways are there to award the prizes if the people holding tickets 19 and 47 both win prizes?  F) How many ways are there to award the prizes if the people holding tickets 19, 47, 73, and 97 all win prizes?  G) How many ways are there to award the prizes if none of the people holding tickets 19, 47, 73, and 97 wins a prize?  H) How many ways are there to award the prizes if the grand prize winner is a person holding ticket 18, 47, 73, or 97?  I) How many ways are there to award the prizes if the people holding tickets 19 and 47 win prizes, but the people holding tickets 73 and 97 do not win prizes? Forgotten PostgreSQL Windows password I have recently found an argument against disabling a root user login in Linux at   I assume that, if everybody uses a public key authentication, there's no risk at losing the root password.  Is it always better to disable the root login via ssh? Is there a way to disable WAC String for a specific link (ex. Tracking Link) with AMPscript or otherwise? Hydrostatic pressure - doesn't density vary with depth? Our class is learning about hydrostatic water pressure and we have been told that we can calculate the force of the liquid on an object at any depth using "the density x 9.8 x the depth". However, as the depth increases, wouldn't the density of the liquid increase because of the weight of the liquid above it compressing it? So should't there be something in the equation to account for the varying density? To me, "density x 9.8 x depth" seems like it is saying that the density will be constant... Some of code I read in trigger is like this    for(account a: [select id  from account where id in: mapAccount.keySet()]) {     //code      }    some are like   List&lt;Account&gt; listAccount = [select id  from account where id in: mapAccount.keySet()];   for(Account a: listAccount ){   //coode   }   Are those same from performance view?which one is better? Random spawn location despite sleeping in a bed I am trying to make Minecraft harder, and one of the ways I wish to do this is to have a "pseudo-hardcore" mode where dying spawns you in a random location rather than completely locking you out of the world.  I intend to do this by setting the spawn radius to be very high.  However, I also want to make this "bed-proof" - that is, if someone places a bed and sleeps in it, I want the player to still be spawned in a random location, regardless of their personal spawn point.  How do I do this? Command blocks are fine, but data packs are not preferred. Which punctuation is correct in this case (colon, semicolon, or period)? Restrictive vs Non-restrictive Relative Clause Cannot remove any bluetooth device Interview: How to ensure that a thread runs after another? How can I change (or remove / reset ) my name on a site in Stack Exchange network? Here $n$ belongs to natural numbers. Firstly, I proved the relation by putting $n = 1$ . Then, taking $$|\sin(mx)| \leq m|\sin x|$$ true, I had to prove $$|\sin(m + 1)x| \leq (m + 1)|\sin x|$$  Now, here I got stuck. How to prove it?? Please help.