In a gambling game you can win a very huge amount of money if you can get 10 consecutive heads tossing a coin. Each toss costs you 1$. How much money will you bet, on average, in order to get 10 consecutive heads?
A fair coin is tossed repeatedly until 5 consecutive heads occurs.   What is the expected number of coin tosses?
Sometimes I'm looking for date-sensitive information and don't want to see results more than a certain age.  Is there a way to specify this in a Google search? Basic Electronics Book I need basic electronics books  (diodes,transistors,current.. etc) as I am just starting out with electronics and want to have something to read over the holiday.  Any suggestions of good beginners' books? What is the "Templates" folder in the home directory for? For as long as I can remember, every time I install Ubuntu there is a folder in the home directory called "Templates." I've always just deleted it, but I'm curious: what's it supposed to be used for, and why is it in the default install? What kind of matter are black holes made of? Can't install jdk on Fedora with yum nor with rpm Suppose you do bad in undergraduate school in say computer science. But you do very well in a masters program in computer science. If you want to apply to a PhD program in computer science, will the masters degree grades offset the undergraduate degree grades? Adding a Link to a Field in a Field Set? String queryFields = null;              for(Schema.FieldSetMember field : SObjectType.Task.FieldSets.Activity_Detail_Page.getFields()){                  queryFields = (queryFields == null ? field.getFieldPath() : queryFields+', '+field.getFieldPath());               }                String query = 'Select '+queryFields+' from Task where Id=\''+activityId+'\'';               task = Database.query(query);   i'll creating a field-set,now how do i add link on any field?  above code is  for dynamically query creation . below code of page   &lt;apex:pageBlock title="Activity" id="Block1"&gt;       &lt;apex:pageBlockSection title="Activity Detail"&gt;         &lt;apex:repeat value="{!$ObjectType.Task.FieldSets.Activity_Detail_Page}" var="field"&gt;             &lt;apex:outputField value="{!Task[field.fieldPath]}" /&gt;         &lt;/apex:repeat&gt;     &lt;/apex:pageBlockSection&gt; &lt;/apex:pageBlock&gt;    As per the image attached, I want to add a link in Rounded field that liks to account. Can any one help me? I am travelling to Athens, Greece, shortly, and have seen . Should I be worried? Should I cancel my trip?  Update  It's fine, taxis are currently on strike, but Syntagma Sqaure is fine: I am using &lt;a&gt; tags for links on a web page. How do I disable the Tab key from selecting either of them? When mounting an NFS share manually using mount and a path of the form &lt;domain/ip&gt;:&lt;path&gt;/&lt;path&gt; or &lt;domain/ip&gt;:/&lt;path&gt;/&lt;path&gt;, umount fails to find the path in /proc/mounts, despite the fact that the path is in fact listed in /proc/mounts.  This is the same problem as in this question:   Steps to reproduce:  # mount --version mount from util-linux 2.24.1 (libmount 2.24.0: debug, assert) # mkdir mountpath # mount 192.168.2.101:/devices mountpath # umount mountpath /home/.../mountpath was not found in /proc/mounts # grep mountpath /proc/mounts 192.168.2.101://devices /home/.../mountpath nfs4 rw,[snip],addr=192.168.2.101 0 0   How can I unmount this mount? How to transpose a dataset in a csv file? Why is usable RAM less than total RAM? My girlfriend bought a laptop last week. It's a core 2 duo with 4 GB  We installed vista 64bit, and one of the first things we did was right click on "My computer" to see gthe properties. Immediately we noticed something strange about her RAM, the line said: Installed memory (RAM): 4,00 GB (3,68 GB usable)  I told her not to worry, thinking it must be something about the laptop hardware (considering her vista installation came from the same DVD as mine, and I never noticed anything like that on my 4 GB desktop). One hour ago, it got worse. We looked at Properties again, and it now says: Installed memory (RAM): 4,00 GB (2,98 GB usable)  What does that mean? Are those 1,02 GB missing or being used by the system?  EDIT: There is a possibility that the sytem information is wrong. I just noticed that it reports an intel T6500 processor, when it's actually a T6400.  How can I find out how much RAM is really available to the system?  EDIT2: Checking the resource monitors, it says 1003 MB are reserved for the hardware. Is that good or bad? Thanks I was trying to give the wording "isomorphic groups have the same structure" a precise interpretation, at least for the finite order case. A positive answer to my final question would reach the goal, as it would translate a "$\cong$" between groups into a "$=$" between sets.    For $n$ positive integer, let be:   $I_n:=\{1,\dots,n\}$; $G$, $\overline G$ groups of order $n$; $\psi\colon G \rightarrow \overline G$ isomorphism; $f$, $\bar f$ bijections; $\theta$, $\bar \theta$ embeddings; in general, $\varphi^{(\alpha)}$ the isomorphism between symmetric groups on sets of the same cardinality, defined by $\sigma \mapsto (g \mapsto (\alpha\sigma\alpha^{-1})(g))$, where $\alpha$ is a bijection between the sets; $S_n$ the symmetric group of degree $n$.   Visually:  $$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}} \begin{array}{c}    I_n     &amp;   &amp;    I_n      \\     \da{f}         &amp;           &amp;     \da{\bar f}          \\    G &amp; \ras{\psi} &amp;    \overline G  \\     \da{\theta}         &amp;           &amp;     \da{\bar \theta}          \\    \operatorname{Sym}(G) &amp; \ras{\varphi^{(\psi)}} &amp;    \operatorname{Sym}(\overline G)  \\     \da{\varphi^{(f)}}         &amp;           &amp;     \da{\varphi^{(\bar f)}}          \\    S_n &amp;  &amp;    S_n  \\ \end{array} $$     Is it $(\varphi^{(f)}\circ\theta)(G)=(\varphi^{(\bar f)}\circ\bar \theta)(\overline G)$? Highest power of a prime $p$ dividing $N!$ Please explain this put option This post is the continuation of another post related to a . Basically, at this point I'm interested in a robust way to discover the periodicity/seasonality of a generic time series affected by a lot of noise. From a developer point of view, I would like a simple interface such as:  unsigned int discover_period(vector&lt;double&gt; v);  Where v is the array containing the samples, and the return value is the period of the signal. The main point is that, again, I can't make any assumption regarding the analyzed signal. I already tried an approach based on the signal autocorrelation (detecting the peaks of a correlogram), but it's not robust as I would like. Sending a message to nil in Objective-C As a Java developer who is reading Apple's Objective-C 2.0 documentation: I wonder what "sending a message to nil" means - let alone how it is actually useful.  Taking an excerpt from the documentation:     There are several patterns in Cocoa   that take advantage of this fact. The   value returned from a message to nil   may also be valid:         If the method returns an object, any pointer type, any integer scalar   of size less than or equal to   sizeof(void*), a float, a double, a   long double, or a long long, then a   message sent to nil returns 0.   If the method returns a struct, as defined by the Mac OS X ABI Function   Call Guide to be returned in   registers, then a message sent to nil   returns 0.0 for every field in the   data structure. Other struct data   types will not be filled with zeros.   If the method returns anything other than the aforementioned value   types the return value of a message   sent to nil is undefined.      Has Java rendered my brain incapable of grokking the explanation above?  Or is there something that I am missing that would make this as clear as glass?  I do get the idea of messages/receivers in Objective-C, I am simply confused about a receiver that happens to be nil. Can I send in for repair a lens that has a shattered front element?     UPDATE: The front element was not shattered, it was the UV filter. Factory diagnosis: Lens assembly had been impacted; cleaned and checked.  Helpful notes by Crowley, David Richerby (x2), Michael Clark (x2), and   mattdm (on element price vs UV filter).      Canon cleaned and checked my lens back to like new quality for $179 labor, no parts, not including shipping.      Jim Garrison answered my question, but Crazy Dino has the best info all around for a lens element shatter.   Original Question:  I recently opened my camera bag to find a shattered front element on a Canon EF 16-35mm f/2.8 L II USM lens.   There are a lot of micro glass shards on the second element.  Does anyone have experience with this sort of thing?  Some of the following are questions I have:   Can I get it repaired? What will the cost be roughly? Will the lens ever work the same and have a good image quality? Should I ship it as is, or attempt cleaning it with air? Where is the best place to cry a little?   Thanks, any good info on this would be appreciated.  I will never rest a lens on another lens, I nearly lost a 24-70mm L that shattered a UV filter also.   Good reason to have a UV always, never thought it could happen to me.  Update: Looking at it more it looks like maybe just the front ring came undone and the UV filter broke?  I can't remember what it looked like exactly before.  I threw away the glass shards (polished sand) in the Nevada desert.      UPDATE: Primary reason for thinking more than just the UV was broken,   UV filter split into two rings, depositing the locking collar into the   lens barrel. What do bookcases do for enchanting? Is there a way to connect my MacBook Pro to two external monitors (either VGA or HDMI; no Thunderbolt) in such a way that the Mac screen serves as a third monitor?  What hardware do I need?