I know the binomial distribution is used to calculate the probability of N heads in M coin tosses. But what if I want to calculate the number of ocurrences of particular pair of events, such as 'HH', in a random string?
I'm trying to find the probability of getting 8 trials in a row correct in a block of 25 trials, you have 8 total blocks (of 25 trials) to get 8 trials correct in a row. The probability of getting any trial correct based on guessing is 1/3, after getting 8 in a row correct the blocks will end (so getting more than 8 in a row correct is technically not possible). How would I go about finding the probability of this occurring? I've been thinking along the lines of using (1/3)^8 as the probability of getting 8 in a row correct, there are 17 possible chances to get 8 in a row in a block of 25 trials, if I multiply 17 possibilities * 8 blocks I get 136, would 1-(1-(1/3)^8)^136 give me the likelihood of getting 8 in a row correct in this situation or am I missing something fundamental here?
biblatex in a nutshell (for beginners) What info does Google backup? Does anyone know what exactly does Google backup (and restore) when you enable that option?  Also, are we able to see this list somewhere? (Maybe hidden n-levels deep in Google Account information?)  Reason I ask is I've had the unfortunate experience of my SD Card dying on me, put in a temporary SD Card and allowed Google to do the auto-restore.  Some things that were restored:   Saved wireless networks Background Some apps - strangely enough only a subset of my apps were restored (some with data, some without). All previous apps were installed via Android Market.   Then finally got my new SD Card, put that in and the following were restored   Saved wireless networks Some apps - again, same problem... only a subset (different subset, even fewer apps). This time no data seemed to have been restored either.   I think it would be very helpful to be able to view/manage a list of what is backed up, and thus would be restored (but I have yet to find this list... if it even exists). Converting string into datetime I've got a huge list of date-times like this as strings:  Jun 1 2005  1:33PM Aug 28 1999 12:00AM   I'm going to be shoving these back into proper datetime fields in a database so I need to magic them into real datetime objects.   This is going through Django's ORM so I can't use SQL to do the conversion on insert. If $\mathfrak p \subset R$ is a prime ideal, prove that for every nilpotent $r \in R$ it follows that $r \in \mathfrak p$.   The only hint that my tutor gave me was to use induction. Can someone explain what he means by this?  Thanks for the help! I just read a book "Linear Algebra and Its Applications 4E" by David C. Lay. The book is (should be) LaTeX typeset. The matrix and equations are so nice, please see the following 3 examples:        It's so beautiful, so I want get the same effect inside my paper. Here is my code:   \usepackage{amsmath} \usepackage{colortbl} \newcommand\y{\cellcolor{clight2}} \definecolor{clight2}{RGB}{212, 237, 244}%  %%% \[A=\left[ \begin{array}{ccccc} \y 0 &amp; -3 &amp; -6 &amp; 4 &amp; 9 \\    -1 &amp; \y -2 &amp; -1 &amp; 3 &amp; 1 \\ -2 &amp; -3 &amp; 0 &amp; \y 3 &amp; -1 \\ 1 &amp; 4 &amp; 5 &amp; -9 &amp; -7      \end{array} \right]\]  \[A=\left[\begin{array}{cccccc} \rowcolor{clight2} 3 &amp; -9 &amp; 12 &amp; -9 &amp; 6 &amp; 15\\ 0 &amp; 2 &amp; -4 &amp; 4 &amp; 2 &amp; -6 \\ 0 &amp; 3 &amp; -6 &amp; 6 &amp; 4 &amp; -5 \end{array} \right]\]   And the result:     But how to add these arrows?? Can anyone suggest a book on using complex numbers to solve geometry problems? Can anyone suggest me a book which includes everything which is needed for solving simple geometry problems through it? I only know about simple calculations on complex numbers. Can I replace a 15 ampere circuit breaker with a 20 ampere breaker? When I plug-in a conventional heating pad or a hair dryer into any bedroom duplex, the lights dim; and/or trips the circuit breaker. The home is of new construction-- placed in service 31 Dec 2013. My question is: Can I safely replace the existing 15 AMP Breaker with that of a 20 AMP? . . . the service cable is of 14 Gauge Copper Conductor. Are there any COGO tools in QGIS 1.9+? The "Azimuth and Distance" plugin does not appear to be maintained any longer, and has not been transitioned to the new QGIS 2.0 plugin repository. What are the current options for entering COGO in QGIS? Does the roadmap include these tools, or is this something that will still depend on a plugin? I've somehow lost my id_rsa.pub file. I still have my id_rsa file. How do I recover the public key from the private key?  (This question came up after ssh-copy-id was reporting "ERROR: No identities found" while ssh-keygen reported "/root/.ssh/id_rsa already exists". ls ~/.ssh pointed out the problem was having id_rsa but not id_rsa.pub. I found the solution, but it was buried at the bottom of a long post on an Ubuntu support forum.) Proof for $e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$ Q1: Could someone provide a proof for this equation (please focus on this question):   $$e^z = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{z}{x} \right)^x$$  Q2: Is there any corelationn between above equation and the equation below (this would benefit me a lot because i at least know how to proove this one):  $$e = \lim \limits_{x \rightarrow \infty} \left( 1 + \frac{1}{x} \right)^x$$ What does "preceding" mean in Oracle? I made my first sculpt model and I used a mirror modifier. But then I applied the mirror modifier, because I got a strange edge on the mirror line in sculpt mode. Now I modeled it, but it still mirrors the model, what in the beginning was good, but sometime I want to do asymmetrical things.  What did I wrong? Many thanks for your help!! Happy modeling :D I just learned about the C++ construct called "placement new".  It allows you to exactly control where a pointer points to in memory.  It looks like this:   #include &lt;new&gt;        // Must #include this to use "placement new"  #include "Fred.h"     // Declaration of class Fred   void someCode()  {    char memory[sizeof(Fred)];    void* place = memory;     Fred* f = new(place) Fred();   // Create a pointer to a Fred(),                                   // stored at "place"     // The pointers f and place will be equal     ...  }    (example from ) In this example, the this pointer of Fred will be equal to place.    I've seen it used in our team's code once or twice.  In your experience, what does this construct enable?  Do other pointer languages have similar constructs?  To me, it seems reminiscent of equivalence in FORTRAN, which allows disparate variables to occupy the same location in memory. How do I update Android on my device? This Community Wiki question is designed to be the "canonical question" for questions asking how to upgrade one's device to a new Android version.   I want to get a newer version of the OS for my Android device. How can I do that?  See also: This is probably a dumb question. I guess what I'm trying to ask is if radio waves travel the same speed as gamma rays, how do gamma photons carry more energy than radio photons? Do they spin faster? What other energy sources could they carry if they are moving the same speed through space? Single Variable Calculus Reference Recommendations This question is a  of the common question asking for calculus references. It is here to  away the repetition, and give a canonical resource for calculus references.      I'm looking for a resources to learn single-variable calculus. What does the term "Extended Partition" mean? Is it safe to use this type of partition? In the image below, what does Extended 103 GB mean? extended stars-and-bars problem(where the upper limit of the variable is bounded) The problem of counting the solutions $(a_1,a_2,\ldots,a_n)$ with integer $a_i\geq0$ for $i\in\{1,2,\ldots,n\}$ such that $$a_1+a_2+a_3+....a_n=N$$ can be solved with a stars-and-bars argument. What is the solution if one adds the constraint that $a_i\leq r_i$ for certain integers $r_1,\ldots,r_n$?  e.g. for $n=3$, $N=6$ and $(r_1,r_2,r_3)=(3,3,2)$, the tuple $(a_1,a_2,a_3)=(2,3,1)$ is a solution, but $(2,1,3)$ is not a solution because $a_3=3&gt;2=r_3$. What is the difference between an abstract method and a virtual method? What is the difference between an abstract method and a virtual method? In which cases is it recommended to use abstract or virtual methods? Which one is the best approach? How to undelete notes on iPhone "Notes" app? iPhone has a default "Notes" app which allows us to store notes. Stored notes can be deleted by hitting the "Delete Note" button:    How do we recover a note that is accidentally deleted?  Is there anyway to undo the delete?